Proportion Word Problems Study Guide (page 2)

Proportions Word Problems

Proportions are extremely helpful when you are solving certain types of math word problems. By using labels and lining them up in proportion, it can become much easier to set up the correct proportion. Read through the following example to practice these techniques and to set the stage for the next practice section. The four steps to solving math word problems are used for each example.

Example 1

Francis can tile 2 square feet of a floor in 20 minutes. At this rate, how long will it take for him to tile 8 square feet?

Read and understand the question. This question is looking for the total amount of time it will take to tile 8 square feet. The time it took to tile 2 square feet is given.

Make a plan. To solve this problem, use a proportion and line up the corresponding labels to put the values in the correct places.

Carry out the plan. The proportion could be set up as:

Notice how the labels match up to help place the values correctly.

Cross multiply the means and the extremes, and solve the equation.

2x = 20 × 8
2x = 160
    Divide each side of the equation by 2.
x = 80 minutes

At the same rate, it would take Francis 80 minutes.

Check your answer. Substitute into the proportion to check that it is a true proportion.

The cross products are each 160. This solution is checking.

Example 2

The ratio of boys to girls in an after-school club is 1 to 3. If there are 21 girls in the club, what is the total number of students in the club?

Read and understand the question. This question is looking for the total number of students in a club. The ratio of boys to girls and the number of girls in the club are given.

Make a plan. To solve this problem, use a proportion and line up the corresponding labels to put the values in the correct places. Be aware that the ratio 1 to 3 represents 1 boy for every 3 girls. This question needs a part to whole ratio. Therefore, use the ratio 3 girls for every 1 + 3 = 4 students.

Carry out the plan. The proportion could be set up as:

Cross multiply the means and the extremes, and solve the equation.

3x = 21 × 4
3x = 84
    Divide each side of the equation by 3.
x = 28 students

There are a total of 28 students in the club.

Check your answer. Substitute into the proportion to check that it is a true proportion.

The cross products are each 84. This solution is checking.

Find practice problems and solutions for these concepts at Proportion Word Problems Practice Questions.