<< Chapter < Page Chapter >> Page >

The ratio of men to women in a particular town is 3 to 5. How many women are there in the town if there are 19,200 men in town?

  • The unknown quantity is the number of women in town.
    Let x = number of women in town.
  • The three specified numbers are
    3
    5
    19,200
  • The comparisons are 3 men to 5 women → 3 5 size 12{ { {3} over {5} } } {}
    19,200 men to x size 12{x} {} women → 19 , 200 x size 12{ { {"19","200"} over {x} } } {}
    3 5 = 19 , 200 x size 12{ { {3} over {5} } = { {"19","200"} over {x} } } {}
  • 3 5 = 19,200 x
    3 x = 19,200 5 3 x = 96,000 x = 96,000 3 x = 32,000
  • There are 32,000 women in town.

The rate of wins to losses of a particular baseball team is 9 2 size 12{ { {9} over {2} } } {} . How many games did this team lose if they won 63 games?

  • The unknown quantity is the number of games lost.
    Let n = number of games lost.
  • Since 9 2 size 12{ { {9} over {2} } } {} → means 9 wins to 2 losses, the three specified numbers are
    9 (wins)
    2 (losses)
    63 (wins)
  • The comparisons are
    9 wins to 2 losses→ 9 2 size 12{ { {9} over {2} } } {}
    63 wins to n size 12{n} {} losses → 63 n size 12{ { {"63"} over {n} } } {}
    9 2 = 63 n size 12{ { {9} over {2} } = { {"63"} over {n} } } {}
  • 9 2 = 63 n
    9 n = 2 63 9 n = 126 n = 126 9 n = 14
  • Step 5: This team had 14 losses.
    Try [link] in [link] .

Practice set a

Solve each problem.

On a map, 3 inches represents 100 miles. How many miles are represented by 15 inches?





















500 miles

An alcohol solution is composed of 14 parts water to 3 parts alcohol. How many parts of alcohol are in a solution that is composed of 112 parts water?





















24 parts of alcohol

A 5 1 2 size 12{5 { {1} over {2} } } {} -foot woman casts a 7-foot shadow at a particular time of the day. How long of a shadow does a 3-foot boy cast at that same time of day?





















3 9 11 size 12{3 { {9} over {"11"} } } {} feet

The rate of houseplants to outside plants at a nursery is 4 to 9. If there are 384 houseplants in the nursery, how many outside plants are there?





















864 outside plants

The odds for a particular event occurring are 11 to 2. (For every 11 times the event does occur, it will not occur 2 times.) How many times does the event occur if it does not occur 18 times?





















The event occurs 99 times.

The rate of passing grades to failing grades in a particular chemistry class is 7 2 size 12{ { {7} over {2} } } {} . If there are 21 passing grades, how many failing grades are there?





















6 failing grades

Exercises

For the following 20 problems, use the five-step method to solve each problem.

On a map, 4 inches represents 50 miles. How many inches represent 300 miles?

24

On a blueprint for a house, 2 inches represents 3 feet. How many inches represent 10 feet?

A model is built to 2 15 size 12{ { {2} over {"15"} } } {} scale. If a particular part of the model measures 6 inches, how long is the actual structure?

45 inches

An acid solution is composed of 5 parts acid to 9 parts of water. How many parts of acid are there in a solution that contains 108 parts of water?

An alloy contains 3 parts of nickel to 4 parts of silver. How much nickel is in an alloy that con­tains 44 parts of silver?

33 parts

The ratio of water to salt in a test tube is 5 to 2. How much salt is in a test tube that contains 35 ml of water?

The ratio of sulfur to air in a container is 4 45 size 12{ { {4} over {"45"} } } {} . How many ml of air are there in a container that contains 207 ml of sulfur?

2328.75

A 6-foot man casts a 4-foot shadow at a particu­lar time of the day. How tall is a person that casts a 3-foot shadow at that same time of the day?

A 5 1 2 size 12{5 { {1} over {2} } } {} -foot woman casts a 1 1 2 size 12{1 { {1} over {2} } } {} -foot shadow at a particular time of the day. How long a shadow does her 3 1 2 size 12{3 { {1} over {2} } } {} -foot niece cast at the same time of the day?

21 22 size 12{ { {"21"} over {"22"} } } {} feet

A man, who is 6 feet tall, casts a 7-foot shadow at a particular time of the day. How tall is a tree that casts an 84-foot shadow at that same time of the day?

The ratio of books to shelves in a bookstore is 350 to 3. How many books are there in a store that has 105 shelves?

12,250

The ratio of algebra classes to geometry classes at a particular community college is 13 to 2. How many geometry classes does this college offer if it offers 13 algebra classes?

The odds for a particular event to occur are 16 to 3. If this event occurs 64 times, how many times would you predict it does not occur?

12

The odds against a particular event occurring are 8 to 3. If this event does occur 64 times, how many times would you predict it does not occur?

The owner of a stationery store knows that a 1-inch stack of paper contains 300 sheets. The owner wishes to stack the paper in units of 550 sheets. How many inches tall should each stack be?

1 5 6 size 12{1 { {5} over {6} } } {}

A recipe that requires 6 cups of sugar for 15 serv­ings is to be used to make 45 servings. How much sugar will be needed?

A pond loses 7 1 2 size 12{7 { {1} over {2} } } {} gallons of water every 2 days due to evaporation. How many gallons of water are lost, due to evaporation, in 1 2 size 12{ { {1} over {2} } } {} day?

1 7 8 size 12{1 { {7} over {8} } } {}

A photograph that measures 3 inches wide and 4 1 2 size 12{4 { {1} over {2} } } {} inches high is to be enlarged so that it is 5 inches wide. How high will it be?

If 25 pounds of fertilizer covers 400 square feet of grass, how many pounds will it take to cover 500 square feet of grass?

31 1 4 size 12{"31" { {1} over {4} } } {}

Every 1 1 2 size 12{1 { {1} over {2} } } {} teaspoons of a particular multiple vitamin, in granular form, contains 0.65 the mini­mum daily requirement of vitamin C. How many teaspoons of this vitamin are required to supply 1.25 the minimum daily requirement?

Exercises for review

( [link] ) Find the product, 818 0 size 12{"818" cdot 0} {} .

0

( [link] ) Determine the missing numerator: 8 15 = N 90 size 12{ { {8} over {"15"} } = { {N} over {"90"} } } {} .

( [link] ) Find the value of 3 10 + 4 12 19 20 size 12{ { { { {3} over {4} } + { {4} over {"12"} } } over { { {"19"} over {"20"} } } } } {} .

2 3 size 12{ { {2} over {3} } } {}

( [link] ) Subtract 0.249 from the sum of 0.344 and 0.612.

( [link] ) Solve the proportion: 6 x = 36 30 size 12{ { {6} over {x} } = { {"36"} over {"30"} } } {} .

5

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Contemporary math applications. OpenStax CNX. Dec 15, 2014 Download for free at http://legacy.cnx.org/content/col11559/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Contemporary math applications' conversation and receive update notifications?

Ask