Algebra-1 Problems

3.8 Proportions
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1.

Solve for x

\begin{equation}\frac{x}{6}=\frac{\frac{5}{2}}{3}\end{equation}

2.

Solve for x

\begin{equation}\frac{x}{48}=\frac{1}{8}\end{equation}

3.

Solve for x

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

4.

Solve for x

\begin{equation}\frac{96}{4}=\frac{8x}{3}\end{equation}

5.

Solve for x

\begin{equation}\frac{5}{x}=\frac{10}{x+8}\end{equation}

6.

Solve for x

\begin{equation}\frac{1}{\frac{11}{5}}=\frac{x}{x+6}\end{equation}

7.

Solve for x

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

8.

Solve for x

\begin{equation}\frac{x}{2}=\frac{\frac{5}{10}}{\frac{2}{10}}\end{equation}

9.

Solve for x

\begin{equation}\frac{x}{\frac{7}{2}}=\frac{\frac{10}{10}}{\frac{5}{10}}\end{equation}

10.

If a car moving at constant speed travels 79 miles in 4 hours, how many miles will it travel in 7 hours?

\begin{equation}\frac{79}{4}=\frac{x}{7}\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 10 pieces of mail in 7 seconds. How many pieces of mail should you be able to sort in 8 minutes?

\begin{equation}\frac{10}{7}=\frac{x}{8 \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 46/13 inches tall.

\begin{equation}\frac{1}{13}=\frac{\frac{46}{13}}{x}\end{equation}

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 60 miles. On the map, how many centimeters are between the two Cities?

\begin{equation}\frac{1}{15}=\frac{x}{60}\end{equation}

14.

The utility worker is 4 ft tall and is casting a shadow 8 ft long. At the same time, a nearby utility pole casts a shadow 10 ft long. Write and solve a proportion to find the height of the utility pole.

\begin{equation}\frac{4}{8}=\frac{x}{10}\end{equation}

15.

A rectangle has an area of 6 sq in. Every dimension of the rectangle is multiplied by a scale factor, and the new rectangle has an area of 24 sq in. What was the scale factor?

\begin{equation}6x^{2}=24\end{equation}