Proportions Word Problems

Proportions are equations that express the equality of two ratios. They are useful in solving word problems involving rates, ratios, and proportions. When you set up a proportion, you can solve for an unknown quantity by cross-multiplying.

Worked Example

Problem: A recipe calls for 3 cups of flour for every 2 cups of sugar. If you want to use 9 cups of flour, how much sugar do you need?

1. Set up the proportion:
   $\frac{3}{2} = \frac{9}{x}$

2. Cross-multiply:
   $3x = 2 \cdot 9$

3. Simplify the right side:
   $3x = 18$

4. Solve for $x$:
   $x = \frac{18}{3}$

5. Simplify:
   $x = 6$

Answer: You need 6 cups of sugar.

Key Questions

• If a car travels 60 miles in 1 hour, how far will it travel in 3 hours?
• A map shows that 1 inch represents 20 miles. How many miles are represented by 5 inches?
• If 4 workers can complete a task in 10 hours, how long will it take 2 workers to complete the same task?
• A recipe requires 2 eggs for every 3 cups of milk. How many eggs do you need for 9 cups of milk?

Keywords

• Proportions
• Ratios
• Rates
• Cross-multiplication
• Word problems