Training Ratios and Proportions Proportion Word Problems
4 / 4

Proportion Word Problems

20 min Ratios and Proportions

More Proportion Word Problems

Proportion word problems challenge you to recognize proportional relationships hidden within everyday language. The key is to read the problem carefully, identify the two ratios being compared, and set them equal before solving.

This lesson presents a collection of proportion word problems of increasing difficulty, covering topics like map distances, speed and time, recipes, and similar figures.

Example 1

A patient takes 250 mg per 50 lbs of body weight. Dosage for a 180-lb patient?

  1. Set up the proportion:
  2. $\dfrac{a}{b} = \dfrac{c}{d}$.
  3. $$\frac{250}{50} = \frac{x}{180} \quad\Longrightarrow\quad 50x = 45{,}000 \quad\Longrightarrow\quad x = 900 \text{ mg}$$
Example 2

$\$1 = €0.92$. How many euros for $\$350$?

  1. Set up the proportion:
  2. $\dfrac{a}{b} = \dfrac{c}{d}$.
  3. $$\frac{0.92}{1} = \frac{x}{350} \quad\Longrightarrow\quad x = €322$$
Example 3

A 6-foot person casts an 8-foot shadow. Same time, a tree casts a 52-foot shadow. How tall?

  1. Set up the proportion:
  2. $\dfrac{a}{b} = \dfrac{c}{d}$.
  3. $$\frac{6}{8} = \frac{x}{52} \quad\Longrightarrow\quad 8x = 312 \quad\Longrightarrow\quad x = 39 \text{ feet}$$
Example 4

A car uses 3 gallons for every 84 miles. How many gallons for a 350-mile trip?

  1. Set up the proportion:
  2. $\dfrac{a}{b} = \dfrac{c}{d}$.
  3. $$\frac{3}{84} = \frac{x}{350} \quad\Longrightarrow\quad 84x = 1050 \quad\Longrightarrow\quad x = 12.5 \text{ gal}$$
Example 5

A survey finds 3 out of 8 people prefer brand X. In a town of 24,000, how many prefer brand X?

  1. Set up the proportion:
  2. $\dfrac{a}{b} = \dfrac{c}{d}$.
  3. $$\frac{3}{8} = \frac{x}{24000} \quad\Longrightarrow\quad x = 9{,}000$$
Strategy for Proportion Problems
  1. Identify the two related pairs of quantities.
  2. Set up the proportion with consistent units on each side.
  3. Cross-multiply and solve.
  4. Check your answer by substituting back.
Interactive Explorer: Recipe Scaler
Scale factor: 2.5×
New quantity: 3.75 cups
Proportion: 1.5/4 = x/10

Practice Problems

1. If 4 tickets cost $\$50$, how much for 10 tickets?
2. A recipe for 8 muffins uses $1\dfrac{1}{2}$ cups flour. Flour for 20 muffins?
3. $\$1 = ¥110$. How many yen for $\$75$?
4. 2 out of 5 students bring lunch. In a school of 800, how many bring lunch?
5. A machine produces 150 parts in 45 min. Parts in an 8-hour shift?
6. Dosage: 5 mL per 25 lbs. Dosage for a 60-lb child?
7. Map scale $1 : 250{,}000$. Cities are 8 cm apart. Actual km?
8. A 5-ft girl's shadow is 3 ft. Flagpole shadow is 18 ft. Height?
9. 15 gallons fills $\dfrac{3}{4}$ of a tank. Tank capacity?
10. Concrete mix: 1 cement, 2 sand, 3 gravel. Cement needed for 18 total cubic ft?
11. Exchange rate: $1 = £0.79$. How many dollars for £500?
12. A car's fuel efficiency is 28 mpg. Gas for a 476-mile trip?
Show Answer Key

1. $\$125$

2. $3\dfrac{3}{4}$ cups

3. $¥8{,}250$

4. $320$

5. $1{,}600$ parts

6. $12$ mL

7. $20$ km

8. $30$ ft

9. $20$ gal

10. $3$ cubic ft

11. $\approx \$632.91$

12. $17$ gal

Applications of Proportions Back to Module