Algebra-1 Problems

3.8 Proportions
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1.

Solve for x

\begin{equation}\frac{x}{7}=\frac{\frac{48}{7}}{6}\end{equation}

2.

Solve for x

\begin{equation}\frac{x}{16}=\frac{1}{4}\end{equation}

3.

Solve for x

\begin{equation}\frac{\frac{5}{7}}{5}=\frac{1}{x}\end{equation}

4.

Solve for x

\begin{equation}\frac{135}{6}=\frac{5x}{2}\end{equation}

5.

Solve for x

\begin{equation}\frac{\frac{3}{2}}{x}=\frac{3}{x+6}\end{equation}

6.

Solve for x

\begin{equation}\frac{1}{\frac{19}{10}}=\frac{x}{x+9}\end{equation}

7.

Solve for x

\begin{equation}\frac{8-x}{10}=\frac{8}{\frac{40}{3}}\end{equation}

8.

Solve for x

\begin{equation}\frac{x}{\frac{12}{5}}=\frac{\frac{10}{10}}{\frac{4}{10}}\end{equation}

9.

Solve for x

\begin{equation}\frac{x}{4}=\frac{\frac{6}{10}}{\frac{6}{10}}\end{equation}

10.

If a car moving at constant speed travels 124 miles in 1 hours, how many miles will it travel in 14 hours?

\begin{equation}\frac{124}{1}=\frac{x}{14}\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 17 pieces of mail in 8 seconds. How many pieces of mail should you be able to sort in 7 minutes?

\begin{equation}\frac{17}{8}=\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 : 17 ft. Estimate the height of the building whose model is 43/17 inches tall.

\begin{equation}\frac{1}{17}=\frac{\frac{43}{17}}{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 7 ft tall and is casting a shadow 8 ft long. At the same time, a nearby utility pole casts a shadow 8 ft long. Write and solve a proportion to find the height of the utility pole.

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

15.

A rectangle has an area of 2 sq in. Every dimension of the rectangle is multiplied by a scale factor, and the new rectangle has an area of 128 sq in. What was the scale factor?

\begin{equation}2x^{2}=128\end{equation}