SOLVING WORD PROBLEMS USING RATIO AND PROPORTION

Set up a proportion to solve each problem, show all work, and label all answers.

Problem 11 :

If a jogger runs 2 miles and burns 185 calories, how many calories would he burn jogging 3 miles?

Solution:

Let x represent the number of calories.

2 : 185 = 3 : x

The jogger will burn 277.5 calories when jogging 3 miles.

Problem 12 :

The ratio of the cost of a tennis racket to tennis balls is 18 : 1. If a can of balls cost $5.35, what is the cost of the racket?

Solution:

Let x represent the cost of the tennis racket.

18 : 1 = x : 5.35

The cost of the tennis racket is $96.30.

Problem 13 :

Curtis School has 1,575 students. The student to teacher ratio is 15 to 1. How many teachers are at Curtis School?

Solution:

let x represent the number of teachers.

15 : 1 = 1575 : x

There are 105 teachers at Curtis school.

Problem 14 :

A recipe calls for 2 1/2 cups of flour to make 2 dozen cookies. How many cups of flour would be required to bake 15 dozen cookies?

Solution:

Let x represent the cups of flour.

2 1/2 : 2 = x : 15

18.75 cups are required to bake 15 dozen of cookies.

Problem 15 :

A meteorologist reports that the ratio of snowfall in January to total snowfall during the average winter is 2 to 5. If 34 inches have fallen in January of the current year, find the predicted total snowfall for the entire winter.

Solution:

Let x be the total snowfall.

2 : 5 = 34 : x

So, the predicted snowfall for the winter is 85 inches.

Problem 16 :

Because of slumping sales, a small company had to lay off some of its employees. The ratio of total employees to employees laid off is 5 to 1. Find the total number of employees if 22 are laid off.

Solution:

Let x be the total number of employees.

5 : 1 = x : 22

So, the total number of employee is 110.

Problem 17 :

A crew of loggers cleared 1/2 acre of lumber in 4 days. How long will it take the same crew to clear 2 3/4 acres of lumber?

Solution:

Let x be the number of days.

1/2 : 4 = 2 3/4 : x

Hence, it take 22 days for the same crew to clear 2 3/4 acres of lumber.

Problem 18 :

A person who weighs 200 pounds on earth would weigh about 32 pounds on the moon. Find the weight of a person on Earth who would weigh 15 pounds of the moon.

Solution:

Let x be the weight of a person on the earth.

200 : 32 = x : 15

So, the weight of a person on the earth is 93.75 lb.

Problem 19 :

A pump can fill a 750-gallon tank in 35 minutes. How long will it take to fill a 1000-gallon tank with this same pump?

Solution:

Let x be the time required to fill the 1000 gallon tank.

750 : 35 = 1000 : x

So, it will take 46 minutes and 40 seconds to fill the larger tank.

Problem 20 :

In a public opinion poll, 624 people from a sample of 1,100 indicated they would vote for a specific candidate. How many votes can the candidate expect to receive from a population of 40,000?

Solution:

Let x represent the number of votes.

624 : 1100 = x : 40000

The candidate can expect about 22,691 votes from a population of 40,000.