### 3.8 Proportions

Problem #

Problem Statement

Problems Similar To

1.

Solve for x

\begin{equation}\frac{x}{4}=\frac{3}{3}\end{equation}

2.

Solve for x

\begin{equation}\frac{x}{56}=\frac{1}{8}\end{equation}

3.

Solve for x

\begin{equation}\frac{3}{6}=\frac{1}{x}\end{equation}

4.

Solve for x

\begin{equation}\frac{6}{3}=\frac{6x}{9}\end{equation}

5.

Solve for x

\begin{equation}\frac{\frac{81}{14}}{x}=\frac{9}{x+5}\end{equation}

6.

Solve for x

\begin{equation}\frac{1}{2}=\frac{x}{x+9}\end{equation}

7.

Solve for x

\begin{equation}\frac{5-x}{3}=\frac{5}{\frac{-15}{2}}\end{equation}

8.

Solve for x

\begin{equation}\frac{x}{\frac{15}{7}}=\frac{\frac{7}{10}}{\frac{5}{10}}\end{equation}

9.

Solve for x

\begin{equation}\frac{x}{4}=\frac{\frac{3}{10}}{\frac{2}{10}}\end{equation}

10.

If a car moving at constant speed travels 62 miles in 4 hours, how many miles will it travel in 12 hours?

\begin{equation}\frac{62}{4}=\frac{x}{12}\end{equation}

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 15 pieces of mail in 9 seconds. How many pieces of mail should you be able to sort in 10 minutes?

\begin{equation}\frac{15}{9}=\frac{x}{10 \times 60}\end{equation}

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 21/13 inches tall.

\begin{equation}\frac{1}{13}=\frac{\frac{21}{13}}{x}\end{equation}

13.

The scale of a map of State X shows that 1 cm represents 7 miles. The actual distance from City A to City B is 28 miles. On the map, how many centimeters are between the two Cities?

\begin{equation}\frac{1}{7}=\frac{x}{28}\end{equation}

14.

The utility worker is 6 ft tall and is casting a shadow 4 ft long. At the same time, a nearby utility pole casts a shadow 6 ft long. Write and solve a proportion to find the height of the utility pole.

\begin{equation}\frac{6}{4}=\frac{x}{6}\end{equation}

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 648 sq in. What was the scale factor?

\begin{equation}8x^{2}=648\end{equation}