Algebra-1 Problems

3.8 Proportions
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1.

Solve for x

\begin{equation}\frac{x}{5}=\frac{\frac{56}{5}}{8}\end{equation}

2.

Solve for x

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

3.

Solve for x

\begin{equation}\frac{1}{10}=\frac{1}{x}\end{equation}

4.

Solve for x

\begin{equation}\frac{40}{10}=\frac{4x}{2}\end{equation}

5.

Solve for x

\begin{equation}\frac{\frac{16}{15}}{x}=\frac{2}{x+7}\end{equation}

6.

Solve for x

\begin{equation}\frac{1}{6}=\frac{x}{x+10}\end{equation}

7.

Solve for x

\begin{equation}\frac{8-x}{7}=\frac{8}{-56}\end{equation}

8.

Solve for x

\begin{equation}\frac{x}{\frac{16}{3}}=\frac{\frac{9}{10}}{\frac{8}{10}}\end{equation}

9.

Solve for x

\begin{equation}\frac{x}{8}=\frac{\frac{7}{10}}{\frac{8}{10}}\end{equation}

10.

If a car moving at constant speed travels 88 miles in 2 hours, how many miles will it travel in 12 hours?

\begin{equation}\frac{88}{2}=\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 14 pieces of mail in 12 seconds. How many pieces of mail should you be able to sort in 7 minutes?

\begin{equation}\frac{14}{12}=\frac{x}{7 \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 : 11 ft. Estimate the height of the building whose model is 2 inches tall.

\begin{equation}\frac{1}{11}=\frac{2}{x}\end{equation}

13.

The scale of a map of State X shows that 1 cm represents 9 miles. The actual distance from City A to City B is 90 miles. On the map, how many centimeters are between the two Cities?

\begin{equation}\frac{1}{9}=\frac{x}{90}\end{equation}

14.

The utility worker is 5 ft tall and is casting a shadow 4 ft long. At the same time, a nearby utility pole casts a shadow 36/5 ft long. Write and solve a proportion to find the height of the utility pole.

\begin{equation}\frac{5}{4}=\frac{x}{\frac{36}{5}}\end{equation}

15.

A rectangle has an area of 7 sq in. Every dimension of the rectangle is multiplied by a scale factor, and the new rectangle has an area of 175 sq in. What was the scale factor?

\begin{equation}7x^{2}=175\end{equation}