### 3.8 Proportions

Problem #

Problem Statement

Problems Similar To

1.

Solve for x

$$\frac{x}{4}=\frac{14}{8}$$

2.

Solve for x

$$\frac{x}{35}=\frac{1}{5}$$

3.

Solve for x

$$\frac{\frac{3}{2}}{3}=\frac{1}{x}$$

4.

Solve for x

$$\frac{\frac{189}{10}}{3}=\frac{7x}{10}$$

5.

Solve for x

$$\frac{\frac{20}{3}}{x}=\frac{10}{x+2}$$

6.

Solve for x

$$\frac{1}{\frac{13}{10}}=\frac{x}{x+3}$$

7.

Solve for x

$$\frac{8-x}{4}=\frac{8}{\frac{32}{5}}$$

8.

Solve for x

$$\frac{x}{\frac{7}{3}}=\frac{\frac{9}{10}}{\frac{3}{10}}$$

9.

Solve for x

$$\frac{x}{\frac{27}{8}}=\frac{\frac{8}{10}}{\frac{9}{10}}$$

10.

If a car moving at constant speed travels 197 miles in 1 hours, how many miles will it travel in 9 hours?

$$\frac{197}{1}=\frac{x}{9}$$

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 8 pieces of mail in 15 seconds. How many pieces of mail should you be able to sort in 2 minutes?

$$\frac{8}{15}=\frac{x}{2 \times 60}$$

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 : 13 ft. Estimate the height of the building whose model is 32/13 inches tall.

$$\frac{1}{13}=\frac{\frac{32}{13}}{x}$$

13.

The scale of a map of State X shows that 1 cm represents 14 miles. The actual distance from City A to City B is 126 miles. On the map, how many centimeters are between the two Cities?

$$\frac{1}{14}=\frac{x}{126}$$

14.

The utility worker is 7 ft tall and is casting a shadow 9 ft long. At the same time, a nearby utility pole casts a shadow 90/7 ft long. Write and solve a proportion to find the height of the utility pole.

$$\frac{7}{9}=\frac{x}{\frac{90}{7}}$$

15.

A rectangle has an area of 5 sq in. Every dimension of the rectangle is multiplied by a scale factor, and the new rectangle has an area of 405 sq in. What was the scale factor?

$$5x^{2}=405$$