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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.

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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] .

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Practice set a

Solve each problem.

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





















500 miles

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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

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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

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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

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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.

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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

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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

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

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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

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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?

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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

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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?

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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

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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?

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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

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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?

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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

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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?

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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

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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?

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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} } } {}

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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?

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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} } } {}

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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?

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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} } } {}

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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?

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Exercises for review

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

0

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

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( [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} } } {}

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

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

5

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Source:  OpenStax, Fundamentals of mathematics. OpenStax CNX. Aug 18, 2010 Download for free at http://cnx.org/content/col10615/1.4
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