### 3.8 Proportions

Problem #

Problem Statement

Problems Similar To

1.

Solve for x

$$\frac{x}{7}=\frac{\frac{12}{7}}{6}$$

2.

Solve for x

$$\frac{x}{40}=\frac{1}{4}$$

3.

Solve for x

$$\frac{1}{2}=\frac{1}{x}$$

4.

Solve for x

$$\frac{\frac{256}{3}}{8}=\frac{8x}{6}$$

5.

Solve for x

$$\frac{\frac{9}{2}}{x}=\frac{9}{x+9}$$

6.

Solve for x

$$\frac{1}{\frac{11}{3}}=\frac{x}{x+8}$$

7.

Solve for x

$$\frac{4-x}{10}=\frac{4}{40}$$

8.

Solve for x

$$\frac{x}{3}=\frac{\frac{10}{10}}{\frac{5}{10}}$$

9.

Solve for x

$$\frac{x}{5}=\frac{\frac{9}{10}}{\frac{5}{10}}$$

10.

If a car moving at constant speed travels 80 miles in 2 hours, how many miles will it travel in 8 hours?

$$\frac{80}{2}=\frac{x}{8}$$

11.

You work in a local mail-room at a college. One of your duties is to sort local mail from all of the other mail. You can sort 16 pieces of mail in 8 seconds. How many pieces of mail should you be able to sort in 5 minutes?

$$\frac{16}{8}=\frac{x}{5 \times 60}$$

12.

An architectural firm makes a model of a science center they are building. The ratio of the model to the actual size is 1 inch : 11 ft. Estimate the height of the building whose model is 37/11 inches tall.

$$\frac{1}{11}=\frac{\frac{37}{11}}{x}$$

13.

The scale of a map of State X shows that 1 cm represents 15 miles. The actual distance from City A to City B is 120 miles. On the map, how many centimeters are between the two Cities?

$$\frac{1}{15}=\frac{x}{120}$$

14.

The utility worker is 5 ft tall and is casting a shadow 10 ft long. At the same time, a nearby utility pole casts a shadow 16 ft long. Write and solve a proportion to find the height of the utility pole.

$$\frac{5}{10}=\frac{x}{16}$$

15.

A rectangle has an area of 8 sq in. Every dimension of the rectangle is multiplied by a scale factor, and the new rectangle has an area of 72 sq in. What was the scale factor?

$$8x^{2}=72$$