Question

proportional relationships practice questions llc

Answer 1

Here are some practice questions focused on proportional relationships. They can be used for individual or group study in a classroom setting or as homework for students:

### Practice Questions on Proportional Relationships

1. **Basic Proportions**
A recipe calls for 3 cups of flour for every 2 cups of sugar.
- a) How much flour is needed for 10 cups of sugar?
- b) If you want to use 9 cups of flour, how much sugar will you need?

2. **Graphing Proportional Relationships**
Plot the points (1, 2), (2, 4), (3, 6), and (4, 8) on a coordinate plane.
- a) Do these points form a straight line?
- b) What is the constant of proportionality?

3. **Real-Life Application**
A car travels 60 miles in 1 hour.
- a) How far will it travel in 3 hours?
- b) If the car travels for 90 miles, how long will it have been traveling?

4. **Unit Rate Problem**
A factory produces 200 widgets in 5 hours.
- a) What is the unit rate of widgets produced per hour?
- b) If the factory operates for 8 hours, how many widgets will it produce?

5. **Determining Proportionality**
The following pairs of numbers are given: (2, 4), (3, 6), (4, 10).
- a) Which of these pairs are proportional?
- b) What is the constant of proportionality for the pairs that are proportional?

6. **Percentage and Proportions**
A store is having a sale where the price of a shirt is reduced by 25%.
- a) If the original price of the shirt is $40, what is the sale price?
- b) What would the sale price be if the original price were $60?

7. **Scale Factor Problem**
A map uses a scale where 1 inch represents 10 miles.
- a) If two cities are 5 inches apart on the map, how far apart are they in reality?
- b) If one city is 30 miles from another city in reality, how far apart would they be on the map?

8. **Solving Proportions**
Solve for \( x \) in the proportion:
\[
\frac{x}{5} = \frac{12}{15}
\]

9. **Word Problem Involving Proportions**
Jenny can read 30 pages in 1 hour. How many pages can she read in 3.5 hours at the same rate?

10. **Comparative Ratios**
If the ratio of boys to girls in a classroom is 2:3 and there are 18 girls, how many boys are there?

### Answers

1.
- a) 15 cups of flour.
- b) 13.5 cups of sugar.

2.
- a) Yes, they form a straight line.
- b) The constant of proportionality is 2.

3.
- a) 180 miles.
- b) 1.5 hours.

4.
- a) 40 widgets/hour.
- b) 320 widgets.

5.
- a) (2, 4) and (3, 6) are proportional.
- b) The constant of proportionality for (2, 4) is 2 and for (3, 6) is 2.

6.
- a) $30.
- b) $45.

7.
- a) 50 miles.
- b) 3 inches.

8.
\( x = 4 \).

9. 105 pages.

10. 12 boys.

Feel free to modify these questions or use them as a basis for your practice on proportional relationships!