CHAPTER 5 RATIO AND PROPORTION - Pearson · 5.1 Ratios 149 CHAPTER 5 RATIO AND PROPORTION 5.1...

5.1 Ratios 149

CHAPTER 5 RATIO ANDPROPORTION

5.1 Ratios5.1 Margin Exercises

1. (a) $ spent on fresh fruit to $ spent on milk( &

(

&

(b) $ spent on milk to $ spent on meat& "%

&

"%

(c) $ spent on meat to $ spent on milk"% &

"%

&

2. (a) hours to hours* "#

* * ƒ $ $

"# "# ƒ $ %œ œ

(b) meters to meters"!! &!

"!! "!! ƒ &! #

&! &! ƒ &! "œ œ

(c) width to length or feet to feet#% %)

#% #% ƒ #% "

%) %) ƒ #% #œ œ

3. (a) The increase in price is

$(Þ!! $ $ .&Þ&! œ "Þ&!

The ratio of increase in price to original price is

."Þ&!

&Þ&!

Rewrite as two whole numbers.

"Þ&! "Þ&! ‚ "!! "&!

&Þ&! &Þ&! ‚ "!! &&!œ œ

Write in lowest terms.

"&! ƒ &! $

&&! ƒ &! ""œ

The decrease in hours is(b)

hours hours hours.%Þ& $ œ "Þ&

The ratio of decrease in hours to the originalnumber of hours is

"Þ&

%Þ&.

Rewrite as two whole numbers.

"Þ& "&

%Þ& %&œ

•

•

"!

"!

Write in lowest terms.

"& ƒ "& "

%& ƒ "& $œ

4. (a) to $ %"#

$

% # " #œ œ ƒ œ

( % (" (# #

%"

•" (

% )œ

pounds to pounds(b) & $& $) %

& y

$œ œ ƒ œ

%& "&

) % )y

& %&) )$ "&% %

%& % $œ

#

y

y

$

# "

"

•"&

inches to inch(c) $" (# )

$ y

œ œ ƒ œ( ( (

# )

y

#y y

" (# #( () )

"

" "

%

•) %

( "œ

5. (a) inches to feet* '

feet ' œ ' • "#œ (#

inches inches

* * * ƒ * "

(# (# (# ƒ * )œ œ œ

inches inches

days to hours(b) # )

days # œ # • #% œ %) hours hours

%) %) %) ƒ ) '

) ) ) ƒ ) "œ œ œ

hours hours

yards to feet(c) ( "%

yards ( œ ( • $ œ #" feet feet

#" #" #" ƒ ( $

"% "% "% ƒ ( #œ œ œ

feet feet

quarts to gallons(d) $ $

gallons $ œ $ • % œ "# quarts quarts

$ $ $ ƒ $ "

"# "# "# ƒ $ %œ œ œ

quarts quarts

minutes to hours(e) #& #

hours# œ # • '!œ "#!

minutes minutes

minutes minutes

#& #& #& ƒ & &

"#! "#! "#! ƒ & #%œ œ œ

(f) pounds to ounces% "#

pounds% œ % • "'œ '%

ounces ounces

ounces ounces

'% '% '% ƒ % "'

"# "# "# ƒ % $œ œ œ

150 Chapter 5 Ratio and Proportion

5.1 Section Exercises

1. ) * œ) )

* * days to days:

days days

3. $ to $"!! &!

$$"!! "!! "!! ƒ &! #

&! &! &! ƒ &! "œ œ œ

5. minutes to minutes$! *!

minutes minutes

$! $! $! ƒ $! "

*! *! *! ƒ $! $œ œ œ

7. miles to miles)! &!

miles miles

)! )! )! ƒ "! )

&! &! &! ƒ "! &œ œ œ

9. hours to hours' "'

hours hours

' ' ƒ # $

"' "' ƒ # )œ œ

11. $ to $%Þ&! $Þ&!

$$%Þ&! %Þ&! %Þ&! %&

$Þ&! $Þ&! $Þ&! $&œ œ œ

œ œ%& ƒ & *

$& ƒ & (

•

•

"!

"!

13. to "& #"#

"& "& &

#œ œ ƒ œ

" # " y" &# #

"&" " # '

& "œ

&y$

"

•

15. to " "" "% #

"

"œ œ ƒ œ

& $ &

% # %y

y" &% %" $# # #

"

•# &

$ 'œ

17. feet to inches% $!

feet% œ % • "# œ %) inches inches

% %) %) %) ƒ ' )

$! $! $! $! ƒ ' &œ œ œ œ

feet inches inches inches

(Do not write the ratio as .)"$&

19. minutes to hour& "

hour minutes" œ '!

minutes minutes

hour minutes& & & & ƒ & "

" '! '! '! ƒ & "#œ œ œ œ

21. hours to days"& #

days# œ # • #% œ %) hours hours

"& "& "& "& ƒ $ &

# %) %) %) ƒ $ "'œ œ œ œ

hours hours days hours

23. gallons to quarts& &

gallons& œ & • % œ #! quarts quarts

& #! #! #! ƒ & %

& & & & ƒ & "œ œ œ œ

gallons quarts quarts quarts

25. Thanksgiving cards to graduation cards

million million

$! $! $! ƒ $! "

'! '! '! ƒ $! #œ œ œ

27. Valentine's Day cards to Halloween cards

million

million*!! *!! *!! ƒ #& $'

#& #& #& ƒ #& "œ œ œ

29. Answers will vary. One possibility is stockingcards of various types in the same ratios as thosein the table.

31. Candle in the Wind White Christmasto

$' $' $' ƒ ' '

$! $! $! ƒ ' &œ œ œ

million million

Candle in the Wind Rock Around the Clockto

$' $'

"( "(œ

millionmillion

33. To get a ratio of , we can start with the smallest$"

value in the table and see if there is a value that isthree times the smallest. and $ ‚ * œ #( #(million is not in the table. , so there$ ‚ "! œ $!are at least pairs of songs that give a ratio of :# $

"

White Christmas It's Now or Never White to and Christmas I Will Always Love You. to $ ‚ "# œ $', Candle inso there is another pair: the Wind I Want to Hold Your Hand. to $ ‚ "( œ &", which is greater than the largestvalue in the table, so we do not need to look forany more pairs.

35. (a) rent to utilities

$$(&! (&! (&! ƒ "#& '

"#& "#& "#& ƒ "#& "œ œ œ

rent to food(b)

$$(&! (&! (&! ƒ "&! &

$!! $!! $!! ƒ "&! #œ œ œ

rent and utilities to total expenses(c)

rent and utilities: $ $ $(&! "#& œ )(&

total expenses:$ $ $ $ $ $##& "#& #!! %!! $!! (&!œ #!!!$

$

$)(& )(& )(& ƒ "#& (

#!!! #!!! #!!! ƒ "#& "'œ œ œ

5.2 Rates 151

37. longest side feetshortest side feet

œ œ( (

& &

The ratio of the length of the longest side to thelength of the shortest side is .(&

39. longest side metersshortest side meters

œ œ"Þ) "Þ)

!Þ$ !Þ$

œ œ œ œ"Þ) ") ") ƒ $ '

!Þ$ $ $ ƒ $ "

•

•

"!

"!

The ratio of the length of the longest side to thelength of the shortest side is .'"

41. longest sideshortest side

inches inches

œ œ œ* *

% %

œ ƒ œ"* "( "*

# % #y

y

" " "*# # #" "% %

"(%

"

#

•% $)

"( "(œ

The ratio of the length of the longest side to thelength of the shortest side is .$)

"(

43. The increase in price is

$ $ $ ."#Þ&! "!Þ!! œ #Þ&!

$

$#Þ&! #Þ&! #Þ&! #&

"!Þ!! "!Þ!! "!Þ!! "!!œ œ œ

œ œ#& ƒ #& "

"!! ƒ #& %

•

•

"!

"!

The ratio of the increase in price to the originalprice is ."%

45. days&* ƒ ( œ"

# # y

" " "(

( #œ

"*y"(

•

"

weeks

weeks weeks

"( "(# #$ $&% %)

œ œ ƒ œ"( $& "(

# % #y

y

"

#

•% $%

$& $&œ

The ratio of days to weeks is .&* )" $ $%# % $&

47. longest sideshortest side

feet feet

œ œ#

#

"

"

("#("#

The ratio of the length of the longest side to thelength of the shortest side is .""

As long as the sides all have the same length, anymeasurement you choose will maintain the ratio.

48. Answers will vary. Some possibilities are:

.% ) "# "' #! #% #)

& "! "& #! #& $! $&œ œ œ œ œ œ

49. It is not possible. Amelia would have to be olderthan her mother to have a ratio of to .& $

50. Answers will vary, but a ratio of to means your$ "income is times your friend's income.$

5.2 Rates5.2 Margin Exercises

1. (a) $ for packages' $!

$ 1 dollar

packages packages' ƒ '

$! ƒ ' &œ

(b) miles in hours&!! "!

&!! ƒ "! &!

"! ƒ "! "œ

miles miles hours hour

(c) teachers for students% *!

% ƒ # #

*! ƒ # %&œ

teachers teachers students students

(d) bushels from acres"#(! $!

"#(! ƒ "! "#(

$! ƒ "! $œ

bushels bushels acres acres

2. $ for pounds of cheese(a) %Þ$& $

$ $ pounds pound%Þ$& ƒ $ "Þ%&

$ ƒ $ "œ

The unit rate is $ /pound."Þ%&

(b) miles on gallons of gas$!% *Þ&

$!% ƒ *Þ& $#

*Þ& ƒ *Þ& "œ

miles miles gallons gallon

The unit rate is miles/gallon.$#

(c) $ in days)&! &

$ $ days day)&! ƒ & "(!

& ƒ & "œ

The unit rate is $ /day."(!

(d) -pound turkey for people#% "&

#% ƒ "& "Þ'

"& ƒ "& "œ

pounds pounds people person

The unit rate is pounds/person."Þ'

3. (a) Size Cost per Unit

quarts #$ quarts

$$Þ#&

#œ "Þ'#&

quarts $$ quarts

$ œ "Þ'&%Þ*&

$

quarts $$ quarts

% œ "Þ'#'Þ%)

%

The lowest cost per quart is $ , so the best"Þ'#buy is quarts for $ .% 'Þ%)


(b) Size Cost per Unit

cans '$ cans

$"Þ**

'¸ !Þ$$#

cans $$

cans"# ¸ !Þ#*"

$Þ%*

"#

cans $$ cans

#% ¸ !Þ#*#(

#%

The lowest price per can is about $ , so!Þ#*"the best buy is cans of cola for $ ."# $Þ%*

4. (a) One battery that lasts twice as long is likegetting two batteries.

$ /battery.$

batteries"Þ"* ƒ #

# ƒ #œ !Þ&*&

The cost of the four-pack is

$ /battery.$

batteries#Þ(* ƒ %

% ƒ %œ !Þ'*(&

The better buy is the single AA-size battery. (b) Brand C: $ $ $$Þ)* !Þ)& œ $Þ!%

$ /ounce$ ounces$Þ!% ƒ '

' ƒ '¸ !Þ&!(

Brand D: $ $ $"Þ&* !Þ#! œ "Þ$*

$ /ounce$ ounces"Þ$* ƒ #Þ&

#Þ& ƒ #Þ&œ !Þ&&'

Brand C with the ¢ coupon is the better buy at)&$ per ounce (rounded).!Þ&!(

5.2 Section Exercises1. cups for people"! '

cups cups

people people"! ƒ # &

' ƒ # $œ

3. feet in seconds"& $&

feet feet

seconds seconds"& ƒ & $

$& ƒ & (œ

5. miles on gallons(# %

miles 4 miles

4 gallons gallon(# ƒ ")

ƒ % "œ

7. $ in hours'! &

$ $ hours hour'! ƒ & "#

& ƒ & "œ

The unit rate is $ per hour or $ /hour."# "#

9. pounds for people(Þ& '

pounds pounds

people person(Þ& ƒ ' "Þ#&

' ƒ ' "œ

The unit rate is pounds person."Þ#& Î

11. $ for days%"$Þ#! %

$ $

days day%"$Þ#! ƒ % "!$Þ$!

% ƒ % "œ

The unit rate is $ day."!$Þ$!Î

13. Miles traveled:

, ,#( (&)Þ# #( %$#Þ$ œ $#&Þ*

Miles per gallon:

miles

gallons$#&Þ* ƒ "&Þ&

"&Þ& ƒ "&Þ&¸ #"Þ!$ ¸ #"Þ!

15. Miles traveled:

, ,#) $*'Þ( #) !&)Þ" œ $$)Þ'

Miles per gallon:

miles

gallons$$)Þ' ƒ "'Þ#

"'Þ# ƒ "'Þ#¸ #!Þ*! ¸ #!Þ*

17. Size Cost per Unit

ounces #$ ounces

$#Þ#&

#œ "Þ"#&

ounces $ $ ounces

% œ !Þ*"#& Ð‡Ñ$Þ'&

%

The best buy is ounces for $ , about% $Þ'&$ ounce.!Þ*"$Î


ounces "#$ ounces

$#Þ%*

"#œ !Þ#!(&

ounces $ $ ounces

"% ¸ !Þ#!'% Ð‡Ñ#Þ)*

"%

ounces $$ ounces

") œ !Þ##$Þ*'

")

The best buy is ounces for $ , about"% #Þ)*$ ounce.!Þ#!'Î


ounces "#$ ounces

$"Þ#*

"#¸ !Þ"!)

ounces $ $ ounces

") ¸ !Þ!** Ð‡Ñ"Þ(*

")

ounces $$ ounces

#) ¸ !Þ"#"$Þ$*

#)

ounces $$ ounces

%! ¸ !Þ""!%Þ$*

%!

The best buy is ounces for $ , about") "Þ(*$ ounce.!Þ!**Î

23. Answers will vary. For example, you mightchoose Brand B because you like more chicken, sothe cost per chicken chunk may actually be thesame or less than Brand A.

5.2 Rates 153

25. pounds in weeks"!Þ& '

pounds pounds

weeks week"!Þ& ƒ ' "Þ(&

' ƒ ' "œ

Her rate of loss was pounds week."Þ(& Î

27. hours to earn $( )&Þ)#

$ $ hours hour)&Þ)# ƒ ( "#Þ#'

( ƒ ( "œ

His pay rate is $ hour."#Þ#'Î

29. (a) Add the connection fee and five times the costper minute.

Radiant Penny:$ $ $ $ $!Þ$* &Ð !Þ!"Ñ œ !Þ$* !Þ!& œ !Þ%%

IDT Special:$ $ $ $ $!Þ"% &Ð !Þ!##Ñ œ !Þ"% !Þ"" œ !Þ#&

Access America:$ $ $ !Þ!! &Ð !Þ!%(Ñ œ !Þ#$&

Divide the total costs by five minutes.(b)

Radiant Penny: $

minutes$ /minute

!Þ%% ƒ &

& ƒ &œ !Þ!))

$ /minute$

minutesIDT Special:

!Þ#& ƒ &

& ƒ &œ !Þ!&

$ /minute$ minutes

Access America: !Þ#$& ƒ &

& ƒ &œ !Þ!%(

Access America is the best buy.

31. Add the connection fee and fifteen (and thentwenty-five) times the cost per minute.

Radiant Penny:$ $ $ $ $!Þ$* "&Ð !Þ!"Ñ œ !Þ$* !Þ"& œ !Þ&%$ $ $ $ $!Þ$* #&Ð !Þ!"Ñ œ !Þ$* !Þ#& œ !Þ'%

IDT Special:$ $ $ $ $!Þ"% "&Ð !Þ!##Ñ œ !Þ"% !Þ$$ œ !Þ%($ $ $ $ $!Þ"% #&Ð !Þ!##Ñ œ !Þ"% !Þ&& œ !Þ'*

Access America:$ $ $!Þ!! "&Ð !Þ!%(Ñ œ !Þ(!&$ $ $!Þ!! #&Ð !Þ!%(Ñ œ "Þ"(&

For the -minute call, IDT Special is the best buy"&at $ . Alternatively, we could calculate the cost!Þ%(per minute to determine the best buy.For the -minute call, Radiant Penny is the best#&buy at $ . !Þ'%

33. One battery for $ is like getting batteries for"Þ(* $$ $ per battery."Þ(* ƒ $ ¸ !Þ&*(

An eight-pack of AAA batteries for $ is%Þ**$ $ per battery.%Þ** ƒ ) ¸ !Þ'#%

The better buy is the one battery package.

35. $ $ coupon $Brand G: #Þ$* !Þ'! œ "Þ(*

$ per ounce$ ounces"Þ(*

"!œ !Þ"(*

$ per ounce$

ouncesBrand K:

$Þ**

#!Þ$¸ !Þ"*(

$ $ coupon $Brand P: $Þ$* !Þ&! œ #Þ)*

$ per ounce$

ounces#Þ)*

"'Þ&¸ !Þ"(&

Brand P with the ¢ coupon has the lowest cost&!per ounce and is the best buy.

37. The one-time activation fee is $ (or $ ) for $& $' "#months.

$

months$ /month

$ $ month)

$& ƒ "#

"# ƒ "#¸ #Þ*#

Ð $'Î"# œ $Î

The activation fee will add $ (rounded) per#Þ*#month for Verizon, T-Mobile, and Nextel; $ per$month for Sprint.

38. Assume there are exactly weeks in a year. Then&#there are &# • & œ #'! weekdays in a year.

#'! ƒ "#

"# ƒ "#¸ #"Þ(

weekdays months

weekdays/month

For Verizon: %!! ƒ #"Þ(

#"Þ( ƒ #"Þ(¸ ")

anytime minutes weekdays

minutes/weekday

For T-Mobile:'!! ƒ #"Þ(

#"Þ( ƒ #"Þ(¸ #)


minutes/weekday

For Nextel and Sprint:&!! ƒ #"Þ(

#"Þ( ƒ #"Þ(¸ #$


minutes/weekday

39. To find the actual average cost per "anytimeminute," add the monthly charge for the activationfee (from Exercise 37) to the monthly charge, thendivide by the number of anytime minutes.

For Verizon:$ $ $

minutes minutes$ /minute

#Þ*# &*Þ** '#Þ*"

%!! %!!œ ¸ !Þ"'

For T-Mobile:$ $ $


#Þ*# $*Þ** %#Þ*"

'!! '!!œ ¸ !Þ!(

For Nextel:$ $ $


#Þ*# %&Þ** %)Þ*"

&!! &!!œ ¸ !Þ"!

For Sprint:$ $ $


$ && &)

&!! &!!œ ¸ !Þ"#

T-Mobile is the best buy at about $ per!Þ!("anytime minute."


40. The total cost is the sum of the activation fee, twomonthly charges, and the termination fee. Thenumber of "anytime minutes" in each case is# ‚ "!! œ #!!.

For Verizon:$ $ $ $

minutes minutes$ minute

$& #Ð &*Þ**Ñ "(& $#*Þ*)

#!! #!!œ

¸ "Þ'&Î

For T-Mobile:$ $ $ $


$& #Ð $*Þ**Ñ #!! $"%Þ*)

#!! #!!œ

¸ "Þ&(Î

For Nextel:$ $ $ $


$& #Ð %&Þ**Ñ #!! $#'Þ*)

#!! #!!œ

¸ "Þ'$Î

For Sprint:$ $ $ $


$' #Ð &&Ñ "&! #*'

#!! #!!œ

œ "Þ%)Î

5.3 Proportions5.3 Margin Exercises

1. (a) $ is to cans as $ is to cans( $ #) "#

$ $

cans cans( #)

$ "#œ

(b) meters is to meters as meters is to * "' ") $#meters

* ")

"' $#œ Common units cancel

(c) is to as is to & ( $& %*

& $&

( %*œ

(d) is to as is to "! $! '! ")!

"! '!

$! ")!œ

2. (a) ' "&

"# $!œ

and ' ƒ ' " "& ƒ "& "

"# ƒ ' # $! ƒ "& #œ œ

Both ratios are equivalent to , so the proportion"#

is true.

(b) #! $

#% %œ

and #! #! ƒ % & $

#% #% ƒ % ' %œ œ

Because is &' not equivalent to , the proportion is$

%

false.

(c) #& $!

%! %)œ

and #& ƒ & & $! ƒ ' &

%! ƒ & ) %) ƒ ' )œ œ

Both ratios are equivalent to , so the proportion&)

is true.

(d) $& "#

%& ")œ

and $& ƒ & ( "# ƒ ' #

%& ƒ & * ") ƒ ' $œ œ

Because is (* not equivalent to , the proportion #

$

is false.

3. (a) & "!

* ")œ

Cross products: & • •") œ *! * "! œ *!;

The cross products are equal, so the proportion istrue.

(b) $# "'

"& )œ

Cross products: $# • •) œ #&' "& "' œ #%!;

The cross products are unequal, so the proportionis false.

(c) "! #!

"( $%œ

Cross products: "! • •$% œ $%! "( #! œ $%!;


(d) #Þ% &

' "#œ

Cross products: ; Ð#Þ%ÑÐ"#Ñ œ #)Þ) ' • & œ $!


(e) $ #%

%Þ#& $%œ

Cross products: $ • $% œ "!# Ð%Þ#&ÑÐ#%Ñ œ "!#;


5.3 Proportions 155

(f) "

#œ

%

)

"'"$

Cross products:

""

' y

y

#"

$

• •

• •

) œ œ( ) #)

' " $

% œ œ( % #)

$ " $

$

%


5.3 Section Exercises1. $ is to cans as $ is to cans.* "# ") #%

$ $ cans cans* ")

"# #%œ

3. adults is to children as adults is to #!! %&! % *children.

adults adults

children children#!! %

%&! *œ

5. feet is to feet as feet is to feet."#! "&! ) "!

"#! )

"&! "!œ The common units (feet) cancel.

7. ' $

"! &œ

and ' ƒ # $ $

"! ƒ # & &œ

Both ratios are equivalent to , so the proportion$&

is true.

9. & #&

) %!œ

and & #& ƒ & &

) %! ƒ & )œ

Both ratios are equivalent to , so the proportion&)

is true.

11. "&! #!!

#!! $!!œ

and "&! ƒ &! $ #!! ƒ "!! #

#!! ƒ &! % $!! ƒ "!! $œ œ

Because is $% not equivalent to , the proportion is#

$

false.

13. %# #)

"& "!œ

and %# ƒ $ "% #) ƒ # "%

"& ƒ $ & "! ƒ # &œ œ

Both ratios are equivalent to , so the proportion"%&

is true.

15. $# %)

") #(œ

and $# ƒ # "' %) ƒ $ "'

") ƒ # * #( ƒ $ *œ œ

Both ratios are equivalent to , so the proportion"'*

is true.

17. ( &%

' %)œ

and ( &% ƒ ' *

' %) ƒ ' )œ

equivalent to , the proportion isBecause is ( *' )not

false.

19. # '

* #(œ

Cross products: # • •#( œ &% * ' œ &%;


21. #! "#

#) "'œ

Cross products: #! • •"' œ $#! #) "# œ $$';


23. ""! "'!

") #(œ

Cross products: ""! • •#( œ #*(! ") "'! œ #))!;


25. $Þ& (

% )œ

Cross products: ; Ð$Þ&ÑÐ)Ñ œ #) % • ( œ #)


27. ") #Þ)

"' #Þ&œ

Cross products: ; ")Ð#Þ&Ñ œ %& "'Ð#Þ)Ñ œ %%Þ)


29. ' ")

$œ

""#$

Cross products:

' $#

$ y• • •"" œ '' ") œ œ ''

"" "

$ ";

"

')y



31. #

$œ

#"

#'

&)"%

Cross products:

#&

) y• •#' œ œ

#" #' #($

) " %%

"$y

$"

%• •#" œ œ

"$ #" #($

% " %


33. #$

# )œ

#Þ(

Cross products:

#

$#Ð#Þ(Ñ œ &Þ%• •) œ œ ¸ &Þ$

# ) "'

$ " $;


35. #

)Þ!& !Þ*œ

$"!

"%

Cross products:

# Ð!Þ*Ñ œ$ #$

"! "!•* #!(

"! "!!œ œ #Þ!(

Ð)Þ!&Ñ œ Ð)Þ!&ÑÐ!Þ#&Ñ œ #Þ!"#&"

%


37. (Answers may vary: proportion may also be setup with "at bats" in both numerators and "hits" inboth denominators. Cross product will be thesame.)

hits hits

at bats at bats

Joe Mauer Freddy Sanchez"( "&$

&! %&!œ

Cross products:"( • •%&! œ ('&! &! "&$ œ ('&!;

The cross products are equal, so the proportion istrue. Paul is correct; the two men hit equally well.

5.4 Solving Proportions5.4 Margin Exercises

1. (a) " B

# "#œ

#

# "y y

# #y yœ

B œ '

• •

• •

B œ " "#

B "#

Cross products are equivalent"

" "

'

We will check our answers by showing that thecross products are equal.

Check: " • •"# œ "# œ # '

(b) ' "&

"! Bœ

'

'

' 'œ

B œ #&

• •

•

B œ "! "&

B

Cross productsare equivalent

y

y y

"

" "

"&!y#&

Check: ' • •#& œ "&! œ "! "&

(c) #) #"

B *œ

B

Bœ

B œ "#

• •

• •

#" œ #) *

#" #) *


y

#" #"y y

y"

" $

%

Check: #) • •* œ #&# œ "# #"

(d) B $

) &œ

B

B #%

& &œ

B œ œ %Þ)#%

&

• •

•

& œ ) $

&


y

y

"

"

Check: Ð%Þ)ÑÐ&Ñ œ #% œ ) • $

5.4 Solving Proportions 157

(e) "% B

"" $œ

""

œ"%

""

B œ ¸ $Þ)#%#

""

• •

• •

B œ "% $

"" B $


y

""y

"

"(rounded to thenearest hundredth)

Check: "% • •$ œ %# œ "" %#""

2. (a) $

# )œ

B

#

#

#

# #œ

B œ "$

"%

• •

• •

•

B œ $ )"

%

B œ"$ )

% "

B #'


y

y

y

y y

"

#

"

" "

y"$

Check: $"% • •) œ #' œ # "$

(b) B

$ &œ

"

&

&

& "

& &œ

B œ "

#$

• •

• •

• •

B œ $ "#

$

B œ $&

$

B &


yy

y y

y y

"

"" "

" "

Check: " • •& œ & œ $ "#$

(c) !Þ!' !Þ$

B !Þ%œ

!Þ$

œ

B œ !Þ!)

• •

•

B œ !Þ!' !Þ%

!Þ$ B !Þ!


y

y y

" !Þ!)

!Þ$ !Þ$" "

#%y

Check: Ð!Þ!'ÑÐ!Þ%Ñ œ !Þ!#% œ Ð!Þ!)ÑÐ!Þ$Ñ

(d) #Þ# "$

& Bœ

#Þ#

œ'&

#Þ#

B œ ¸ #*Þ&&'&

#Þ#

• •

•

B œ & "$

# B


Þ#y

y

"

#Þ#"

(rounded to thenearest hundredth)

Check: #Þ# œ '& œ &ˆ ‰'&#Þ# • "$

(e)B !Þ&

' "Þ#œ

"Þ#

œ œ œ$ $! &

"Þ# "# #

B œ #Þ&

•

•

B œ 'Ð!Þ&Ñ

" B


Þ#y

y

"

"Þ#"

Check: Ð#Þ&ÑÐ"Þ#Ñ œ $ œ 'Ð!Þ&Ñ

(f) ! B

# (Þ!*#œ

Since , !# œ ! B must equal . The denominator!

(Þ!*# ! could be any number (except ).


1. " B

$ "#œ

$

$ "#y

$ $yœ

B œ %

• •

•

B œ " "#

B


"

"

We will check our answers by showing that thecross products are equal.

Check: " • •"# œ "# œ $ %

3. OR "& $ $ $

"! B # Bœ œ

Since the numerators are equal, the denominatorsmust be equal, so .B œ #

5. OR B $# B )

"" % "" "œ œ

"

B œ ))

• •B œ "" )Cross productsare equivalent

Check: )) • •% œ $&# œ "" $#


7. %# ")

B $*œ

B

Bœ

y

B œ *"

• •

• •

") œ %# $*

" % $


) # *y y

y y

y"

"

( "$

'") ")

"

Check: %# • •$* œ "'$) œ *" ")

9. OR B % B "

#& #! #& &œ œ

&

&y

& &y yœ

B œ &

• •

•

B œ #& "

B #


"

" "

&&y

Check: & • •#! œ "!! œ #& %

11. OR ) #% ) %

B $! B &œ œ

%

% )y

% %y yœ

y

B œ "!

• •

• •

B œ ) &

B &


"

" "

#

Check: ) • •$! œ #%! œ "! #%

13. OR ** %% * %%

&& B & Bœ œ

*

* ##!y

* *yœ

B œ##!

*¸ #%Þ%%

• •

•

B œ & %%

B


"

"

Check: ** • •##!* œ #%#! œ && %%

15. !Þ( $Þ'

*Þ) Bœ

!Þ(

!œ

&

B œ &!Þ%

•

•

B œ *Þ) Ð$Þ'Ñ

! B $


Þ( &Þ#)y

y y

" !Þ%

Þ( !Þ(" "

y

Check: !Þ(Ð&!Þ%Ñ œ $&Þ#) œ *Þ)Ð$Þ'Ñ

17. #&! B

#%Þ) "Þ(&œ

#%Þ)

# #%Þ)œ

%$(Þ&

¸ "(Þ'%

•

•

B œ #&!Ð"Þ(&Ñ

# B


%Þ)y

y

"

%Þ)"

Check: #&!Ð"Þ(&Ñ œ %$(Þ& œ #%Þ) • %$(Þ&#%Þ)

19. "& *

"œ

B

"&

"&y

y

œ"&

"&

B œ "

#$

• •

• •

•

B œ " *#

$

B œ& *

$ "

" B


"

$

"

"

&y

y"&

21. #

" #œ

B

""

#

$

# y

y

$

#

œ

B œ ƒ œ#" $

% # %y

y

y

"$" "# %

$ #"# %$ $# #

• •

• •

•

•

•

B œ # #" "

$ %

B œ( *

$ %

B œ#"

%B

# # ( "

$ # #œ œ $

"

$

(

#

"

"

"y

23. Change to a decimal by dividing: "# " ƒ # œ !Þ&

"#

B !Þ)œ

#

!Þ& #

B !Þ)œ

B

B

B !Þ%y

#yœ

#

B œ !Þ#

••

•

# œ !Þ&Ð!Þ)Ñ

# œ !Þ%

#"

"

Now change to a fraction and write it in lowest!Þ)terms:

5.4 Solving Proportions 159

!Þ) œ œ) ƒ # %

"! ƒ # &

Bœ

#

By

y

B

B y

#yœ

#

B œ ƒ # œ# #

& &

y

y

"#

%&

#&

• •

•

•

•

# œ" %

# &

# œ#

&

#

" "

#œ

&

"

#

"

""

"

25. B !Þ"&

œ"$

&!%&

Change to decimals.

B !Þ"&

!Þ!' "Þ)œ

BB !Þ!!*

"Þ) "Þ)œ

B œ !Þ!!&

••"Þ) œ !Þ"&Ð!Þ!'Ñ"Þ)

Change to fractions.

B

œ"

"%

&"

" "œ

B œ ƒ " œ* % *

"!!! & "

y y

y

$&!

$#!%&

% *& "!!!% %& &

• •

•

•

B œ$ $

&! #!B

& "

* #!!œ

" "

#!! "!!!y

27. "! &

% $œ

Find the cross products.

"!

%

••

$ œ $!

& œ #!

The cross products are unequal, so the proportionis true.not

Replace with ."! B

B &

% $œ

$

B œ œ '#! #

$ $'

% $œ

&

• •B œ % &

, so

is a true proportion.#$

Replace with .% B

"! &

B $œ

&

B œ œ '$!

&"! &

' $œ

• •B œ "! $

, so

is a true proportion.

Replace with .& B

"! B

% $œ

%

B œ œ œ (Þ&$! "&

% #"! (Þ&

% $œ

• •B œ "! $

, so


Replace with . $ B"! &

% Bœ

"!

B œ œ ##!

"!"! &

% #œ

• •B œ % &

, so


28. ' #%

) $!œ

Find the cross products.

'

)

••$! œ ")!

#% œ "*#

The cross products are unequal, so the proportionis true.not

Replace with .' B

B #%

) $!œ

$!

B œ œ œ 'Þ%) $#

$! &

'Þ% #%

) $!œ

• •

•

B œ ) #%

#%y

y

%

&

, so


continued


Replace with .) B

' #%

B $!œ

#%

B œ œ œ (Þ&' $!

# %

' #%

(Þ& $!œ

• •

•

B œ ' $!

$!y

y

&

%%

, so


Replace with .#% B

' B

) $!œ

)

B œ œ œ ##Þ&' %&y

) #yy

' ##Þ&

) $!œ

• •

•

B œ ' $!

$$ "&

%#

!y, so


Replace with .$! B

' #%

) Bœ

'

B œ œ $#)

'y

' #%

) $#œ

• •

•

B œ ) #%

#%y%

"

, so


Summary Exercises on Ratios, Rates, andProportions

1. freshmen to juniors#%!! #!!!

#%!! #%!! ƒ %!! '

#!!! #!!! ƒ %!! &œ œ

3. seniors and sophomores to ")&! #"&! #!!!juniors

")&! #"&! %!!! %!!! ƒ #!!! #

#!!! #!!! #!!! ƒ #!!! "œ œ œ

5. (i) million violin players to million piano# ##players

million

# # ƒ # "

## ## ƒ # ""œ œ

million

(ii) million violin players to million guitar# #!players

million

# # ƒ # "

#! #! ƒ # "!œ œ

million

(iii) million violin players to million organ# 'players

million

# # ƒ # "

' ' ƒ # $œ œ

million

(iv) million violin players to million clarinet# %players

million

# # ƒ # "

% % ƒ # #œ œ

million

(v) million violin players to million drum# $players

million

# #

$ $œ

million

7. points points

minutes minutes points minute

"!! "!! ƒ %)

%) %) ƒ %)œ

œ #Þ!)$ ¸ #Þ" Î

minutes minutes

points points minute point

%) %) ƒ "!!

"!! "!! ƒ "!!œ

œ !Þ%) ¸ !Þ& Î

9. $ hour$ $

hours hours'&#Þ)! '&#Þ)! ƒ %!

%! %! ƒ %!œ œ "'Þ$#Î

Her regular hourly pay rate is $ hour."'Þ$#Î

$ hour$ $

hours hours"*&Þ)% "*&Þ)% ƒ )

) ) ƒ )œ œ #%Þ%)Î

Her overtime hourly pay rate is $ hour.#%Þ%)Î


ounces ""$ ounces

$'Þ(*

""¸ !Þ'#

ounces $ $ ounces

"# œ !Þ'! Ð‡Ñ(Þ#%

"#

ounces $$ ounces

"' ¸ !Þ'*"!Þ**

"'

The best buy is ounces for $ , about $"# (Þ#% !Þ'!per ounce.

13. #) %%

#" $$œ

and #) ƒ ( % %% ƒ "" %

#" ƒ ( $ $$ ƒ "" $œ œ

Both ratios are equivalent to , so the proportion%$

is true.

5.5 Solving Application Problems with Proportions 161

15. #

$œ

#"

#'

&)"%

Cross products:

#&

) y• •#' œ œ

#" #($

) " %%

#'y"$

$"

%• •#" œ œ

"$ #" #($

% " %


17. "& '

) Bœ

"&

œ œ œ $Þ#) "'y

&

• •

• •

B œ ) '

B '


"&y

y y

" #

" &"& "&

Check: "&Ð$Þ#Ñ œ %) œ ) • '

19. "! B

"" %œ

""

œ ¸ $Þ'%%!

""

• •

•

B œ "! %

B


""y

y

"

"""

Check: "! • •% œ %! œ "" %!""

21. #Þ' "$

B (Þ)œ

"$

œ œ "Þ&'#!Þ#)

"$

•

•

B œ #Þ'Ð(Þ)Ñ

B


"$y

y

"

""$

Check: #Þ'Ð(Þ)Ñ œ #!Þ#) œ "Þ&'Ð"$Ñ

23. "$

) #%œ

B

)

) )y

) )yœ œ "

• •

•

B œ #%"

$

B


"

"

Check: "$ Ð#%Ñ œ ) œ ) • "

5.5 Solving Application Problemswith Proportions

5.5 Margin Exercises

1. pounds pounds

square feet square feet(a)

# B

&! ##&œ

&!

&! %&!

&! &!œ

B œ *

• •

•

B œ # ##&

B


Divide both sides by 50

pounds of fertilizer are needed for square* ##&feet.

inch inches miles miles

(b) " %Þ(&

(& Bœ

miles

"

B œ $&'Þ#& ¸ $&'

•B œ (&Ð%Þ(&ÑCross productsare equivalent

The lake's actual length is about miles.$&'

milliliters milliliters

pounds pounds(c)

$! B

"!! $%œ

milliliters

"!!

"!! "!#!

"!! "!!œ

B œ "!Þ# ¸ "!

• •

•

B œ $! $%

B



A -pound child should be given about $% "!milliliters of cough syrup.

2. people people people

(a) # B

$ "&!œ

$

$ $!!

$ $œ

B œ "!!

• •

•

B œ # "&!

B



In a group of , people want to lose weight."&! "!!This is a reasonable answer because it's more thanhalf the people, but less than all the people.

Incorrect setup

$ B

# "&!œ

## %&!

# #œ

B œ ##&

people people people

• ••B œ $ "&!B

The incorrect setup gives an answer of people,##&which is unreasonable since there are only "&!people in the group.


FA students

students students(b)

$ B

& %&!!œ

,

&

& "$ &!!

& &œ

B œ #(!!

• •

•

B œ $ %&!!

B



At Central Community College students#(!!receive financial aid. This is a reasonable answerbecause it's more than half the people, but lessthan all the people.

Incorrect setup

students

FA students students

,

& B

$ %&!!œ

$$ ## &!!

$ $œ

B œ (&!!

• ••B œ & %&!!B

The incorrect setup gives an answer of (&!!students, which is unreasonable since there areonly students at the college.%&!!

sugarless

dentists dentists(c)

* B

"! '!œ

"!

"! &%!

"! "!œ

B œ &%

• •

•

B œ * '!

B



If the advertisement is true, of the dentists in&% '!the city would recommend sugarless gum. This isa reasonable answer since it is almost all of thedentists.

Incorrect setup

"! B

* '!œ

** '!!

* *œ

B œ ''Þ' ¸ '(

• ••B œ "! '!B

The incorrect setup gives an answer of dentists,'(which is unreasonable since there are only '!dentists in the city.


1. hours hours

cartoon strips cartoon strips& B

% ")œ

& B

% ")œ

%

%

% *!y

%yœ

%

B œ ##Þ&

• ••

•

B œ & ")

B œ *!

B"

"

It will take hours to sketch cartoon strips.##Þ& ")

3. newspapers newspapers

$'! "'

#( Bœ

'!'! %$#

'! '!œ

B œ (Þ#

• ••B œ #( "'B

The cost of newspapers is $ ."' (Þ#!

5. pounds square feet square feet

,

$ B

$&! %*!!œ

$&!$&! "% (!!

$&! $&!œ

B œ %#

• ••B œ $ %*!!B

pounds are needed to cover square feet.%# %*!!

7. $

days days'(#Þ)! B

& $œ

&& #!")Þ%!

& &œ

B œ %!$Þ')

••B œ Ð'(#Þ)!ÑÐ$ÑB

In days Tom makes $ .$ %!$Þ')

9. ounces

servings servings' B

( "#œ

(( (#

( (œ

B œ "! ¸ "!#

(

• ••B œ ' "#B

You need about ounces for servings."! "#

11. quarts

square feet square feet$ B

#(! Ð$&! "!!Ñœ

$ B

#(! %&!œ

#(!#(! "$&!

#(! #(!œ

B œ &

• ••B œ $ %&!B

You will need quarts.&


13. First find the length.

inch inches feet

" $Þ&

% Bœ

"

B œ "%

•B œ %Ð$Þ&Ñ

The kitchen is feet long."%

Then find the width.

inch inches feet feet

" #Þ&

% Bœ

"

B œ "!

•B œ %Ð#Þ&Ñ

The kitchen is feet wide."!

15. The length of the dining area is the same as thelength of the kitchen, which is feet by Exercise"%13.

Find the width of the dining area.

inches inches inch inches feet

%Þ& #Þ& œ #

" #

% Bœ

"

B œ )

• •B œ % #

The dining area is feet wide.)

17. Set up and solve a proportion with pieces ofchicken and number of guests.

pieces guests guests

pieces of chicken

%! B

#& '!œ

#&#& %!

#& #&œ

B œ œ *'%!

#&

• •• •

•

B œ %! '!B '!

'!

For the other food items, the proportions aresimilar, so we simply replace " " in the last step%!with the appropriate value.

pounds of lasagna"%

#&œ $$Þ'

• '!

pounds of deli meats%Þ&

#&œ "!Þ)

• '!

pounds of cheese($ • '!

#& & &œ œ &

#) $

dozen (about buns dozen$

#&œ (Þ# )'Ñ

• '!

pounds of salad'

#&œ "%Þ%

• '!

19. refresher entering entering

,

( B

"! #*&!œ

"!"! #! '&!

"! "!œ

B œ #!'&

• ••B œ ( #*&!B

students will probably need a refresher#!'&course. This is a reasonable answer because it'smore than half the students, but not all thestudents.

Incorrect setup

"! B

( #*&!œ

(( #* &!!

( (œ

B ¸ %#"%

entering refresher entering

,• ••B œ "! #*&!B

The incorrect setup gives an estimate of %#"%entering students, which is unreasonable sincethere are only entering students.#*&!

21. chooses vanilla choose vanilla

people people" B

$ #&!œ

$$ #&!

$ $œ

B ¸ )$Þ$ ¸ )$

• ••B œ " #&!B

You would expect about people to choose)$vanilla ice cream. This is a reasonable answer.

Incorrect setup

$ B

" #&!œ

"

B œ (&!

people choose vanilla chooses vanilla people

• •B œ $ #&!

With an incorrect setup, people choose vanilla(&!ice cream. This is unreasonable because only #&!people attended the ice cream social.

23. , ,

,, , ,

, ,

*) B

"!! ""$ "!! !!!œ

"!! ""$ ""!! "" !)$ )!! !!!

"!! "!!œ

B œ ""! )$) !!!

• ••B œ *) !! !!!B

,

, , U.S. households have one or more""! )$) !!!TVs.

continued


Incorrect setup

"!! B

*) ""$ "!! !!!œ

*) ""$ "!! !!!*) "" $"! !!! !!!

*) *)œ

B ¸ ""& %!) "'$

, ,, ,

, , ,

, ,

• ••B œ "!!B

The incorrect setup gives about , , U.S.""& %!) "'$households with one or more TVs, but there areonly , , U.S. households.""$ "!! !!!

25. stocks up stocks up

stocks down stocks down& B

' (&!œ

& B

' (&!œ

'' $(&!

' 'œ

B œ '#&

• ••B œ & (&!B

stocks went up.'#&

27. length meters length width meters width

) $#Þ&

" Bœ

)

) $#Þ&y

) )yœ

B œ %Þ!'#& ¸ %Þ!'

• •

•

B œ " $#Þ&

B"

"

The wing must be about meters wide.%Þ!'

29. pounds pounds calories

,

"&! #"!

### Bœ

"&!"&! %' '#!

"&! "&!œ

B œ $"!Þ) ¸ $""

• ••B œ ### #"!B

A -pound person would burn about #"! $""calories.

31. meters meters meters

"Þ!& 'Þ&)

"Þ') Bœ

"Þ!&"Þ!& ""Þ!&%%

"Þ!& "Þ!&œ

B œ "!Þ&#) ¸ "!Þ&$

••B œ "Þ')Ð'Þ&)ÑB

The height of the tree is about meters."!Þ&$

33. You cannot solve this problem using a proportionbecause the ratio of age to weight is not constant.As Jim's age increases from to years old, his#& &!weight may decrease, stay the same, or increase.

35. First find the number of coffee drinkers.

,

,

,

% B

& &! &!!œ

&& #!# !!!

& &œ

B œ %! %!!

• ••B œ % &! &!!B

,

The survey showed that , students drink%! %!!coffee. Now find the number of coffee drinkerswho use cream.

,

,

" B

) %! %!!œ

)) %! %!!

) )œ

B œ &!&!

••B œ %! %!!B

,

According to the survey, students use cream.&!&!

37. First find the number of calories in a -cup"#

serving of bran cereal.

cup

calories cup"

$"#

"$" "$ $

)! Bœ

"

$

œ œ%! %!

"

B œ "#!

• •

••

B œ )!"

#B $

"

Then find the number of grams of fiber in a -cup"#

serving of bran cereal.

cup

grams of fiber cup"

$"#

"$" "$ $

) Bœ

"

$

œ œ% %

"

B œ "#

• •

••

B œ )"

#B $

"

A -cup serving of bran cereal provides "# "#!

calories and grams of fiber."#


39. Use proportions.

Water: $

"# 'œ

B

"#

"#

"# #"

"# "#œ

B œ œ "( $

% %

"# cups

servings servings

• •

• •

•

B œ $ '"

#

B œ '(

#B

Margarine: Tbsp


"# 'œ

"#"# $'

"# "#œ

B œ $

• ••B œ ' 'B

Milk: cups

servings servings"

"# 'œ

B

"#

"#

"# *

"# "#œ

B œ$

%

"#

• •

• •

•

B œ " '"

#

B œ '$

#B

Potato flakes: cups

servings servings% B

"# 'œ

"#"# #%

"# "#œ

B œ #

• ••B œ % 'B

Multiply the quantities by (or divide by ), since"# #

6 servings is of 12 servings. "#

Water: $

# # # #œ œ ƒ # œ

( (

œ œ "( $

% %

" (# # •

"

#

Margarine: '

#œ $

Milk: "

# # #œ œ ƒ #

$

œ$

#

" $# #

•" $

# %œ

Potato flakes: %

#œ #

For servings, use cups water, Tbsp' " $$%

margarine, cup milk, and cups potato flakes.$% #

40. Use proportions.

Water: $

"# ")œ

B

"#

"#

"# '$

"# "#œ

B œ &"

%

"# cups

servings servings

• •

• •

•

B œ $ ")"

#

B œ ")(

#B

Margarine: Tbsp


"# ")œ

"#"# "!)

"# "#œ

B œ *

• ••B œ ' ")B

Milk: cups

servings servings"

"# ")œ

B

"#

"#

"# #(

"# "#œ

B œ #"

%

"#

• •

• •

•

B œ " ")"

#

B œ ")$

#B

Potato flakes: cups

servings servings% B

"# ")œ

"#"# (#

"# "#œ

B œ '

• ••B œ % ")B

Multiply the quantities in Exercise 39 by 3, since18 servings is 3 times 6 servings.

Water: "$

%• •$ œ œ œ &

( $ #" "

% " % %

Margarine: $ • $ œ *

Milk: $

%• •$ œ œ œ #

$ $ * "

% " % %

Potato flakes: # • $ œ '

For servings, use cups water, Tbsp") & *"%

margarine, cups milk, and cups potato flakes.# '"%


41. Since servings is of servings, multiply each$ '"#

quantity in Exercise 39 by ."#

Water: "$

%• •" ( " (

# % # )œ œ

Margarine: $ • •" $ " $ "

# " # # #œ œ œ "

Milk: $

%•" $

# )œ

Potato flakes: # • •" # "

# " #œ œ "

For servings, use cup water, Tbsp$ "( ") #

margarine, cup milk, and cup potato flakes.$) "

42. Since servings is times servings, multiply* $ $each quantity in Exercise 41 by .$

Water: (

)• •$ œ œ œ #

( $ #" &

) " ) )

Margarine: $ $ $ * "

# # " # #$ œ œ œ %• •

Milk: $

)• •$ œ œ œ "

$ $ * "

) " ) )

Potato flakes: " • $ œ $

For servings, use cups water, Tbsp* # %& ") #

margarine, cups milk, and cups potato flakes." $")

Chapter 5 Review Exercises1. orca whale's length to whale shark's length

ft ft

$! $! $! ƒ "! $

%! %! %! ƒ "! %œ œ œ

2. blue whale's length to great white shark's length

ft ft

)! )! )! ƒ #! %

#! #! #! ƒ #! "œ œ œ

3. To get a ratio of , we can start with the smallest"#

value in the table and see if there is a value that istwo times the smallest. , so the ratio# ‚ #! œ %!of the great white shark's whale length to the shark's length is . The length of the orca#! "

%! #œ

whale is ft, but $! # ‚ $! œ '! is not in the table.# ‚ %! œ )!, whale shark'sso the ratio of the length to the length is .blue whale's %! "

)! #œ

4. $ to $#Þ&! "Þ#&

$$#Þ&! #Þ&! #Þ&! ƒ "Þ#& #

"Þ#& "Þ#& "Þ#& ƒ "Þ#& "œ œ œ

5. $ to $!Þ$! !Þ%&

$$!Þ$! !Þ$! !Þ$! ƒ !Þ"& #

!Þ%& !Þ%& !Þ%& ƒ !Þ"& $œ œ œ

6. cups to cup"# #$ $

cups cup

" "œ œ ƒ

& #

$ $

œ&

$y

y

# #$ $# #$ $

"

"

•$ &

# #œ

7. miles to miles# "'$ "% #

miles miles

# #

"' "'œ œ œ ƒ

"" $$

% #

œ%y

y

$ $ ""% % %" " $$# # #

""y

y

" "

# $

•# "

œ'$$

8. hours to minutes& "!!

hours & œ & • '! œ $!! minutes minutes

$!! $!! $!! ƒ "!! $

"!! "!! "!! ƒ "!! "œ œ œ

minutes minutes

9. inches to feet* #

feet inches# œ #%

inches inches

* * * ƒ $ $

#% #% #% ƒ $ )œ œ œ

10. ton to pounds" "&!!

ton pounds" œ #!!!

pounds pounds

#!!! #!!! #!!! ƒ &!! %

"&!! "&!! "&!! ƒ &!! $œ œ œ

11. hours to days) $

days$ œ $ • #% œ (# hours hours

) ) ) ƒ ) "

(# (# (# ƒ ) *œ œ œ

hours hours

12. Ramona's $ to Jake's $&!! $&!

$$&!! &!! ƒ &! "!

$&! $&! ƒ &! (œ œ

The ratio of Ramona's sales to Jake's sales is ."!(

13. miles per gallon miles per gallon

$& $& $& ƒ & (

#& #& #& ƒ & &œ œ œ

The ratio of the new car's mileage to the old car'smileage is .(

&

14. students students

'!!! '!!! '!!! ƒ "#!! &

(#!! (#!! (#!! ƒ "#!! 'œ œ œ

The ratio of the math students to the Englishstudents is .&'

15. $ for dozen)) )

$ $

dozen dozen)) ƒ ) ""

) ƒ ) "œ

Chapter 5 Review Exercises 167

16. children in families*' %!

children children families families

*' ƒ ) "#

%! ƒ ) &œ

17. pages in minutes% #!

pages page minutes minute

page minute

or page minute

(i) % ƒ #! !Þ#

#! ƒ #! "œ

œ !Þ# Î"

&Î

minutes minutes pages page

minutes page

(ii) #! ƒ % &

% ƒ % "œ

œ & Î

18. $ in hours#% $

$ hour$ $ hours hour

(i) #% ƒ $ )

$ ƒ $ "œ œ )Î

hours hour$ $

hour dollar

or hour dollar

(ii) $ ƒ #% !Þ"#&

#% ƒ #% "œ

œ !Þ"#& Î"

)Î


ounces )$ ounces

$ %Þ*)

)¸ !Þ'#$ Ð‡Ñ

ounces $$ ounces

$ œ !Þ)$#Þ%*

$

ounces $$ ounces

# œ !Þ*%&"Þ)*

#

The best buy is ounces for $ , about) %Þ*)$ ounce.!Þ'#$Î

20. pounds for $ $ (coupon) $$&Þ# $'Þ*' " œ $&Þ*'

$$

pounds$&Þ*'

$&Þ#¸ "Þ!##

pounds for $ $ (coupon) $"(Þ' ")Þ'* " œ "(Þ'*

$ $

pounds"(Þ'*

"(Þ'¸ "Þ!!& Ð‡Ñ

pounds for $$Þ& %Þ#&

$$ pounds%Þ#&

$Þ&¸ "Þ#"%

The best buy is pounds for $ 8 with the"(Þ' " Þ'*$ coupon, about $ pound." "Þ!!&Î

21.

and

' *

"! "&œ

' ƒ # $ * ƒ $ $

"! ƒ # & "& ƒ $ &œ œ

Both ratios are equivalent to , so the proportion$&

is true.

22. ' *

%) $'œ

Cross products: ' • •$' œ #"' %) * œ %$#;


23. %( *)

"! #!œ

Cross products: %( • •#! œ *%! "! *) œ *)!;


24.

and

'% *'

$' &%œ

'% ƒ % "' *' ƒ ' "'

$' ƒ % * &% ƒ ' *œ œ

Both ratios are equivalent to , so the proportion"'*

is true.

25. "Þ& #

#Þ% $Þ#œ

Cross products: "Þ&Ð$Þ#Ñ œ %Þ) #Þ% ); • # œ %Þ


26. $

#œ

'

%

"#"$

Cross products:

$"

# y

y• •% œ œ "%

( %

# ""

#

#"

$ y

y• •' œ œ "%

( '

$ ""

#


27. OR % "&! # "&!

%# B #" Bœ œ

#

# $"&!

# #œ

B œ "&(&

• •

•

B œ #" "&!

B


Check: % • •"&(& œ '$!! œ %# "&!

28. OR "' "# "' %

B "& B &œ œ

%

% )!

% %œ

B œ #!

• •

•

B œ & "'

B


Check: "' • •"& œ #%! œ )! %


29. OR "!! B &! B

"% &' ( &'œ œ

(

( #)!!

( (œ

B œ %!!

• •

•

B œ &! &'

B


Check: "!! • •&' œ &'!! œ "% %!!

30. & B

) #!œ

)

) "!!

) )œ

B œ "#Þ&

• •

•

B œ & #!

B


Check: & • #! œ "!! œ )Ð"#Þ&Ñ

31. B ""

#% ")œ

")

") #'%

") ")œ

B œ ¸ "%Þ'(%%

$

• •

•

B œ #% ""

B


Check: %%$ • •") œ #'% œ #% ""

32. OR ( ") ( '

B #" B (œ œ

'

' %*

' 'œ

B œ ¸ )Þ"(%*

'

• •

•

B œ ( (

B


Check: ( • •#" œ "%( œ ")%*'

33. B *Þ)

$Þ' !Þ(œ

!Þ( œ *Þ)Ð$Þ'Ñ

!Þ( $&Þ#)

!Þ( !Þ(œ

B œ &!Þ%

•

•

B

B


Check: &!Þ%Ð!Þ(Ñ œ $&Þ#) œ $Þ'Ð*Þ)Ñ

34. "$Þ& %Þ&

"Þ( Bœ

"$Þ& B œ "Þ(Ð%Þ&Ñ

"$Þ& (Þ'&

"$Þ& "$Þ&œ

B ¸ !Þ&(

•

•


B

Check: "$Þ& œ (Þ'& œ "Þ(Ð%Þ&Ñˆ ‰(Þ'&"$Þ&

35. !Þ)# B

"Þ)* &Þ(œ

"Þ)*

"Þ)* %Þ'(%

"Þ)* "Þ)*œ

B ¸ #Þ%(

•

•

B œ !Þ)#Ð&Þ(Ñ

B


Check: !Þ)#Ð&Þ(Ñ œ %Þ'(% œ "Þ)*ˆ ‰%Þ'(%"Þ)*

36. cats dogs dogs$ B

& %&œ

&& "$&

& &œ

B œ #(

• ••B œ $ %&B

There are cats.#(

37. hits

at bats at bats) B

#) "'"œ

#)#) "#))

#) #)œ

B œ %'

• ••B œ ) "'"B

She will get hits.%'

38. pounds pounds$

$Þ& &Þ'

*Þ(( Bœ

$Þ&$Þ& &%Þ("#

$Þ& $Þ&œ

B ¸ "&Þ'$

••B œ *Þ((Ð&Þ'ÑB

The cost for pounds of ground beef is $&Þ' "&Þ'$(rounded).

39. voting students

students students

,

% B

"! )#%(œ

"!"! $# *))

"! "!œ

B ¸ $#**

• ••B œ % )#%(B

They should expect about students to vote.$#**

40. inch inches feet

" %Þ#&

"' Bœ

"

B œ ')

•B œ "'Ð%Þ#&Ñ

The length of the real boxcar is feet.')

Chapter 5 Review Exercises 169

41. dozen necklaces# œ # • "# œ #% necklaces

#% %!

"'œ

B

#%

#% ''!

#% #%œ

B œ #(Þ& œ #("

#

necklaces necklaces hours"

#

• • •

•

B œ "' %! œ" $$ %!

# # "B

It will take Marvette hours or hours to#( #(Þ&"#

make necklaces.%!

42. calories

minutes minutes

,

#)% B

#& %&œ

#&#& "# ()!

#& #&œ

B œ &""Þ# ¸ &""

• ••B œ #)% %&B

A -pound person would burn about ")! &""calories in minutes.%&

43. milligrams

pounds pounds$Þ& B

&! #"!œ

&!&! ($&

&! &!œ

B œ "%Þ(

• ••B œ $Þ& #"!B

A patient who weighs pounds should be given#"!"%Þ( milligrams of the medicine.

44. [5.4] OR B (! B (

%& $! %& $œ œ

$

$ $"&

$ $œ

B œ "!&

• •

•

B œ ( %&

B


Check: "!& • •$! œ $"&! œ %& (!

45. [5.4] B !

&# #!œ

Since , !#! œ ! B must equal . The denominator ! &#

could be any number (except ).!

46. [5.4] OR '% B $# B

"! #! & #!œ œ

&

& '%!

& &œ

B œ "#)

• •

•

B œ $# #!

B


Check: '% • •#! œ "#)! œ "! "#)

47. [5.4] OR "& '& "& "$

B "!! B #!œ œ

"$

"$ $!!

"$ "$œ

B œ ¸ #$Þ!)$!!

"$

• •

•

B œ "& #!

B


Check: "& • •"!! œ "&!! œ '&$!!"$

48. [5.4] OR (Þ) "$ # "$

$Þ* B " Bœ œ

## "$

# #œ

B œ 'Þ&

• ••B œ " "$B

Check: (Þ)Ð'Þ&Ñ œ &!Þ( œ $Þ* • "$

49. [5.4] $%Þ" !Þ((

B #Þ'&œ

!Þ((!Þ(( *!Þ$'&

!Þ(( !Þ((œ

B ¸ ""(Þ$'

••B œ $%Þ"Ð#Þ'&ÑB

Check: $%Þ"Ð#Þ'&Ñ œ *!Þ$'& œ Ð!Þ((Ñˆ ‰*!Þ$'&!Þ((

50. [5.3] && )!

") #(œ

Cross products: && • •#( œ "%)& ") )! œ "%%!;


51. [5.3] &Þ' ")

!Þ' "Þ*%œ

Cross products:&Þ'Ð"Þ*%Ñ œ "!Þ)'%; !Þ' œ "!Þ)• ")


52. [5.3] " "& '

#$

#œ

"

""

Cross products:

"

& y• •"" œ œ œ #

# " ( "

$ & $ $ $"

($&y

#y

y• •1

" # ( ( "

' " ' $ $œ œ œ #

"

$



53. [5.1] dollars to quarters% "!

dollars% œ % • % œ "' quarters

"' ƒ # )

"! ƒ # &œ

quarters quarters

54. [5.1] inches to inches% "!")

inches inches

%

"! "! )œ œ ƒ "!

$$

œ$$

)

" $$) )

•" $$

"! )!œ

55. [5.1] yards to feet"! )

yards"! œ "! • $ œ $! feet

$! $! ƒ # "&

) ) ƒ # %œ œ

feet feet

56. [5.1] $ to $$Þ'! !Þ*!

$$$Þ'! $Þ'! ƒ !Þ*! %

!Þ*! !Þ*! ƒ !Þ*! "œ œ

57. [5.1] eggs to eggs"# "&

eggs eggs

"# "# ƒ $ %

"& "& ƒ $ &œ œ

58. [5.1] meters to meters$( (

meters

meters$( $(

( (œ

59. [5.1] pints to quarts$ %

quarts% œ % • # œ ) pints

$ $

) )œ

pints pints

60. [5.1] minutes to hours"& $

hours$ œ $ • '! œ ")! minutes

"& "& ƒ "& "

")! ")! ƒ "& "#œ œ

minutes minutes

61. [5.1] miles to miles% "" $# "!

miles miles

% %

" "œ œ % ƒ "

" $

# "!

œ ƒ œ* "$ *

# "! #y

œ%&

"$

" "# #$ $"! "!

"

&

•"!y

"$

62. [5.5] ( B

) #) &!!œ

)) "** &!!

) )œ

B ¸ #% *$(Þ& #% *!!

buying fans fans , fans

,

, or ,(

• ••B œ ( #) &!!B

,

rounded to the nearest hundredÑ

At today's concert, about , fans can be#% *!!expected to buy a beverage.

63. [5.1]

$ spent on car insurance

$ spent on repairs%!! %!! ƒ &! )

"&! "&! ƒ &! $œ œ

The ratio of the amount spent on insurance to theamount spent on repairs is .)$

64. [5.2] feet for $#& !Þ()

$ per foot$

feet!Þ()

#&¸ !Þ!$"

feet for $ $ (coupon) $(& "Þ** !Þ&! œ "Þ%*

$ per foot ( )$

feet"Þ%*

(&¸ !Þ!#! ‡

feet for $ $ (coupon) $"!! #Þ&* !Þ&! œ #Þ!*

$ per foot$

feet#Þ!*

"!!¸ !Þ!#"

The best buy is feet for $ with a ¢(& "Þ** &!coupon, about $ foot.!Þ!#!Î

65. [5.5] First find the length.

inch inches

feet!Þ& "Þ(&

' Bœ

!Þ&!Þ& "!Þ&

!Þ& !Þ&œ

B œ #"

••B œ 'Ð"Þ(&ÑB

When it is built, the actual length of the patio willbe feet.#"

Then find the width.

inch inches

feet!Þ& "Þ#&

' Bœ

!Þ&!Þ& (Þ&

!Þ& !Þ&œ

B œ "&

••B œ 'Ð"Þ#&ÑB

When it is built, the actual width of the patio willbe feet."&

Chapter 5 Test 171

66. [5.5] gallons gallons hours

or

!Þ) #

$ Bœ

!Þ)!Þ) '

!Þ) !Þ)œ

B œ (Þ& ("

#

• ••B œ $ #B

The lawn mower should run or hours on a(Þ& ( "#

full tank.

67. [5.5] teaspoons pounds pounds

or

"

#% )œ

B

#%

#% "#

#% #%œ

B œ !Þ&"

#

"#

• • •

•

B œ " ) œ œ œ "#" $ ) #%

# # " #B

The infant should be given or teaspoon."# !Þ&

68. [5.5] points

minutes minutes#&" B

"'* "%œ

"'*"'* $&"%

"'* "'*œ

B ¸ #!Þ(*#)**

• ••B œ #&" "%B

Charles should score points (rounded).#"

69. [5.5] Set up the proportion to compare teaspoonsto pounds on both sides.

"Þ& B

#% )œ

tsp tsp pounds pounds

Show that the cross products are equal.

Ð#%ÑÐBÑ œ Ð"Þ&ÑÐ)Ñ

Divide both sides by .#%

, so tsp or tspÐ#%Ñy ÐBÑ "# "

#%yœ B œ !Þ&

#% #

"

"

70. [5.5] milligrams pounds pounds

(a) "!!! B

& (œ

&& (!!!

& &œ

B œ "%!!

• ••B œ "!!! (B

A -pound cat should be given milligrams.( "%!!

ounces pound pound(b) ) œ œ !Þ&)"'

milligrams pounds pounds

"!!! B

& !Þ&œ

&& &!!

& &œ

B œ "!!

••B œ "!!!Ð!Þ&ÑB

An -ounce kitten should be given milligrams.) "!!

Chapter 5 Test1. fish to fish"' #!

fish fish

"' "' ƒ % %

#! #! ƒ % &œ œ

2. miles on gallons$!! "&

miles miles

gallons gallon$!! ƒ "& #!

"& ƒ "& "œ

3. $ for minutes"& (&

$ $

minutes minutes"& ƒ "& "

(& ƒ "& &œ

4. hours to minutes$ %!

hours$ œ $ • '! œ ")! minutes minutes

")! ")! ƒ #! *

%! %! ƒ #! #œ œ

minutes minutes

5. seats

seats"#!! "#!! ƒ )! "&

$#! $#! ƒ )! %œ œ


Small $ inches

$ inch%Þ$*

&œ !Þ)()Î

Regular $ inch$ inches&Þ(*

)¸ !Þ(#%Î Ð‡Ñ

Large $ inch$

inches)

""¸ !Þ(#(Î

The best buy is the -inch sub, which costs about)$ per inch.!Þ(#%

7. ounces of Brand X for#'$ $ (coupon) $$Þ)* !Þ(& œ $Þ"%

$ per ounce$ ounces$Þ"%

#'¸ !Þ"#"

"' ounces of Brand Y for$ $ (coupon) $"Þ)* !Þ&! œ "Þ$*

$ per ounce ( )$ ounces"Þ$*

"'¸ !Þ!)( ‡

ounces of Brand Z for $ ."% "Þ#*

$ per ounce$ ounces"Þ#*

"%¸ !Þ!*#

The best buy is ounces of Brand Y for $"' "Þ)*with a ¢ coupon, about $ ounce.&! !Þ!)(Î

8. You earned less this year. An example is:

$ ,$ ,

Last yearThis year

ÄÄ

œ$

#

$! !!!

#! !!!


9. ' ")

"% %&œ

Cross products: ' • •%& œ #(! "% ") œ #&#; The cross products are unequal, so the proportion

is We could also write the fractions infalse.lowest terms to see that they are not equalˆ ‰$ #( &Á .

10. )Þ% #Þ"

#Þ) !Þ(œ

$ $

" "œ Write in lowest terms

The proportion is true. We could also show thatthe cross products are equal .Ð&Þ))Ñ

11. & B

* %&œ

*

* ##&

* *œ

B œ #&

• •

•

B œ & %&

B


Check: & • •%& œ ##& œ * #&

12. $ )

" Bœ

$

$ )

$ $œ

B ¸ #Þ'(

• •

•

B œ ) "

B


Check: $Ð Ñ œ ) œ ")$ • )

13. B 'Þ&

#! !Þ%œ

!Þ%

!Þ% "$!

!Þ% !Þ%œ

B œ $#&

•

•

B œ #!Ð'Þ&Ñ

B


Check: $#&Ð!Þ%Ñ œ "$! œ #!Ð'Þ&Ñ

14. #

B %œ

)

*

œ

B œ ƒ œ#) )

$ * $y y

y

" )$ *

) #)* $) )* *

• • •

•

•

B œ # % œ œ" ( % #)

$ $ " $B

# * #" "

) # #œ œ "!

)y( $

" #

Check: #"$ • •% œ œ#) #" )

$ # *

15. orders

minutes minutes") B

$! %!œ

$!$! (#!

$! $!œ

B œ #%

• ••B œ ") %!B

Pedro could enter orders in minutes.#% %!

16. ounce

square feet square feet!Þ) B

&! ##&œ

&!&! ")!

&! &!œ

B œ $Þ'

••B œ !Þ)Ð##&ÑB

ounces of wildflower seeds are needed for a$Þ'garden with square feet.##&

17. left-handed people

people students# B

"& '&!œ

"&"& "$!!

"& "&œ

B œ ¸ )(#'!

$

• ••B œ # '&!B

You could expect about students to be)(left-handed.

18. No, cannot be correct because there are only%)(&'&! students in the whole school.

19. grams

pounds pounds)Þ# B

&! "%&œ

&!&! "")*

&! &!œ

B œ #$Þ() ¸ #$Þ)

••B œ )Þ#Ð"%&ÑB

A -pound person should be given grams"%& #$Þ)(rounded).

20. inch inchesfeet

" (Þ&

) Bœ

"

B œ '!

•B œ )Ð(Þ&Ñ

The actual height of the building is feet.'!

Cumulative Review Exercises (Chapters 1–5) 173

Cumulative Review Exercises(Chapters 1–5)

1. to the nearest hundred**!$Draw a cut-off line: **l!$The first digit cut is , which is or less. The part! %you keep stays the same. **!!

2. to the nearest tenth:'"(Þ!&"*Draw a cut-off line: '"(Þ!l&"*The first digit cut is or more, so round up.&'"(Þ"

3. $ to the nearest dollar:**Þ)"Draw a cut-off line: $**Þl)"The first digit cut is or more, so round up. & $"!!

4. $ to the nearest cent:$Þ!&&&Draw a cut-off line: $$Þ!&l&&The first digit cut is or more, so round up.&$$Þ!'

5. $! !Þ''

/ / / //

$!Þ ! !

!Þ ' '

#*Þ $ %

#**"!"!

6. R ,' " ! #(

$$ # ! " & (" * )

$ &$ $

# (!

# (

7. Ð"Þ*ÑÐ!Þ!!%Ñ

"Þ* Ã "

‚ !Þ!!% Ã $

!Þ!!(' Ã %

decimal placedecimal placesdecimal places

8. $!#! (!)

/ / //$ ! # !

( ! )

# $ " #

#"!" "!

9. !Þ%!" '#Þ*) &

!Þ%!"

'#Þ*)!

&Þ!!!

')Þ$)"

Write in 0's

10. "Þ$* ƒ !Þ!#&

^ ^

& &Þ '

!Þ!#& "Þ $ * ! !" # &

" % !" # &

" & !" & !

!

Move decimal point indivisor and dividend

Write 0 inthe dividend

11. $' ") ƒ ' œ $' Ð") ƒ 'Ñ œ $' $ œ $*

12. ) ƒ % "! $

œ ) ƒ % "

œ # "

œ # "' œ ")

ˆ ‰# • •

••

% œ ) ƒ % Ð"! *Ñ "'

"'

"'

#

13. )) ƒ

œ )) ƒ ""

œ )

È È"#" "#"• ••

•

# œ )) ƒ )

)

) œ '%

$

14. Ð"'Þ# &Þ)&Ñ #Þ$&Ð%Ñ œ "!Þ$& #Þ$&Ð%Ñ

œ "!Þ$& *Þ% œ !Þ*&

15. is one hundred five ten-thousandths.!Þ!"!&

16. Sixty and seventy-one thousandths is .'!Þ!("

17. don't drink coffee to total

Total œ #&! #!! &&! œ "!!!

#!! #!! ƒ #!! "

"!!! "!!! ƒ #!! &œ œ

18. drink coffee to don't drink coffee

&&! #&! )!! )!! ƒ #!! %

#!! #!! #!! ƒ #!! "œ œ œ

19. First get a decimal representation for each mixednumber.

" œ "Þ & ' # &* #&

"' "'"' # &Þ ! ! ! !

" '

* !) !

" ! !* '

% !$ #

) !) !

!

" ¸ "Þ&'$*"'

continued


1 $ ""

) )œ "Þ $ ( &

) " "Þ ! ! !)

$ !# %

' !& '

% !% !

!

" œ "Þ$(&$)

1 " *

) )œ "Þ " # &

) *Þ ! ! !)

" !)

# !" '

% !% !

!

" œ "Þ"#&")

Now compare all the numbers.

"Þ& œ "Þ&!!

" ¸ "Þ&'$*

"'"Þ#& œ "Þ#&!

" œ "Þ$(&$

)

" œ "Þ"#&"

)

largest

smallest

The nest box openings (in inches) in order fromsmallest to largest are:

" "Þ#& " "Þ& "" $ *) ) "', , , ,

20. 1* * " * )

"' "' # "' "' "Þ& œ " " œ " "

œ œ œ#& #% #& #% "

"' "' "' "'

" œ "Þ&'#&*

"' "Þ& œ "Þ&!!!

!Þ!'#&

The difference is inch or about inch.""' !Þ!'$

21. OR * B $ B

"# #) % #)œ œ

%

% )%

% %œ

B œ #"

• •

•

B œ $ #)

B


Divide bothsides by 4

Check: * • •#) œ #&# œ "# #"

22. ( "!

"# Bœ

(

( "#!

( (œ

B ¸ "(Þ"%

• •

•

B œ "! "#

B


Divide bothsides by 7

Check: ( œ "#! œ "#ˆ ‰"#!( • "!

23. 'Þ( '#Þ)

B *Þ"&œ

'#Þ)'#Þ) '"Þ$!&

'#Þ) '#Þ)œ

B ¸ !Þ*)

••B œ 'Þ(Ð*Þ"&ÑB

Check: 'Þ(Ð*Þ"&Ñ œ '"Þ$!& œ '#Þ)ˆ ‰'"Þ$!&'#Þ)

24. Find the amount already collected.

&

'y

"&!! "#&! œ #&!"

•"

"œ "#&!

&!!y#&!

They need to collect pounds.#&!

25. cm wide cm long cm long

"! B

"& %!œ

"&"& %!! )!

"& "& $œ œ

B ¸ #'Þ(

• ••B œ "! %!B

The enlarged width of the photo is #'Þ(centimeters (rounded).

26. First add the number of times Norma ran in themorning and in the afternoon.

Then multiply the sum by the distance around Dunning Pond.

% # œ '" "

# #

""

"!• •' œ œ œ (

" "" "$ "%$ $

# "! # #! #!

Norma ran miles.( $#!

Cumulative Review Exercises (Chapters 1–5) 175

27. servings for $"( "Þ(&

$ per serving$ servings"Þ(&

"(¸ !Þ"!$

servings for $ $ (coupon) $$% $Þ)& !Þ&! œ $Þ$&

$ per serving ( )$ servings$Þ$&

$%¸ !Þ!** ‡

servings for $ $ (coupon) $%# %Þ(& !Þ&! œ %Þ#&

$ per serving$ servings%Þ#&

%#¸ !Þ"!"

The best buy is servings for $ with a ¢$% $Þ)& &!coupon, about $ serving.!Þ!**Î

28. bothered residents

residents residents& B

) ##%œ

)) ""#!

) )œ

B œ "%!

• ••B œ & ##%B

You would expect residents to be bothered by"%!noise.

29. teaspoon

quarts water quarts water

"#

&#

# &œ

B

#

#

# #œ

B œ ƒ # œ& &

# #

• •

•

•

B œ &"

#B

" & "

# % %œ œ "

Use teaspoons of plant food.""%

30. The cost per minute rates (in dollars) from least togreatest are:

, , , , , , !Þ!#) !Þ!% !Þ!%$ !Þ!& !Þ!&# !Þ"!' !Þ"#

31. minutes$

$ /minute"! "!

!Þ!%$ !Þ!%$œ ¸ #$#Þ'

You could make a call to Japan for minutes#$$(rounded).

32. minutes$

$ /minute"!

!Þ"#¸ )$Þ$

You get minutes (rounded) per $ card,)$ "!so buy cards ( minutes) to cover$ #%*#%! % minutes ( hours).

33. For South Korea:

minutes$

$ /minute"!

!Þ!%œ #&!

For Mexico City:

$

$ /minute minutes

"!

!Þ!&œ #!!

Ratio of minutes to South Korea tominutes to Mexico City:

#&! ƒ &! &

#!! ƒ &! %œ

The ratio of minutes for a $10 call to South Koreato minutes for a $10 call to Mexico is .City &

%

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