Ratio word problems

This lesson will show you how to solve four easy ratio word problems and three challenging ratio word problems that require more thinking.

Interesting ratio word problems

Example #1:

In a small business, 40 of the employees are men and 30 of the employees are women. What is ratio of women to men?

Solution:

The ratio of women to men is 30 to 40, 30:40, or 30/40

Example #2:

The length of a rectangular garden is 20 feet and the width is 15 feet. What is ratio of length to width?

Solution:

The ratio of length to width is 20 to 15, 20:15 or 20/15

Example #3:

A hybrid car can go 400 miles on 8 gallons of gas. How far can the car take you with 1 gallon of gas?

Solution:

Although the problem does not say to find the ratio, it is a ratio word problem. What you need to do is to first write the ratio of number of miles the car can travel to the number of gallons of gas the car has. Then, write the ratio in simplest form.

The ratio is 400/8 and in simplest form it is 50/1 after dividing both numerator and denominator by 8.

So you can go 50 miles on 1 gallon of gas.

A simple ratio word problem

Hard ratio word problems

Example #4:

Suppose the width of a soccer field 60 meters and the length is 100 meters. What is the ratio in simplest form of the length to the area of the field?

Solution:

The area of the field is 60 × 100 = 6000

The ratio of the length to the area is 100 to 6000, 100:6000 or 100/6000

100/6000 = 1/60

The ratio of the length to the area in simplest form is 1/60

Example #5:

A geometry test has 30 questions. 6 of the 30 questions are based on chapter 5. What is the ratio of questions from chapter 5 to the other questions on the test?

Solution:

There are a total of 30 - 6 or 24 other questions on the geometry test.

The ratio of questions from chapter 5 to other questions on the test is 6:24 or 6/24

Example #6:

Suppose a math class starts at the beginning of the school year with 12 boys and 8 girls. However, after school resumes in January, 6 new boys and 4 new girls came to the class. Is the ratio of boys to total number of students in the class still the same? 

Solution:

Ratio of boys to total number of students at the beginning of the school year is 12/8 or 3/2 in simplest form.

Ratio of boys to total number of students after school resumes in January is (12 + 6)/(8 + 4) = 18/12 or 3/2 in simplest form.

Therefore, the ratio is still the same.

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