Algebra-1 Problems

3.8 Proportions
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1.

Solve for x

\begin{equation}\frac{x}{10}=\frac{\frac{14}{5}}{4}\end{equation}

2.

Solve for x

\begin{equation}\frac{x}{27}=\frac{1}{3}\end{equation}

3.

Solve for x

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

4.

Solve for x

\begin{equation}\frac{84}{6}=\frac{7x}{5}\end{equation}

5.

Solve for x

\begin{equation}\frac{4}{x}=\frac{9}{x+5}\end{equation}

6.

Solve for x

\begin{equation}\frac{1}{\frac{11}{4}}=\frac{x}{x+7}\end{equation}

7.

Solve for x

\begin{equation}\frac{8-x}{3}=\frac{8}{-12}\end{equation}

8.

Solve for x

\begin{equation}\frac{x}{\frac{45}{4}}=\frac{\frac{8}{10}}{\frac{9}{10}}\end{equation}

9.

Solve for x

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

10.

If a car moving at constant speed travels 152 miles in 2 hours, how many miles will it travel in 6 hours?

\begin{equation}\frac{152}{2}=\frac{x}{6}\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 6 seconds. How many pieces of mail should you be able to sort in 2 minutes?

\begin{equation}\frac{15}{6}=\frac{x}{2 \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 : 14 ft. Estimate the height of the building whose model is 47/14 inches tall.

\begin{equation}\frac{1}{14}=\frac{\frac{47}{14}}{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 6 ft tall and is casting a shadow 7 ft long. At the same time, a nearby utility pole casts a shadow 35/3 ft long. Write and solve a proportion to find the height of the utility pole.

\begin{equation}\frac{6}{7}=\frac{x}{\frac{35}{3}}\end{equation}

15.

A rectangle has an area of 4 sq in. Every dimension of the rectangle is multiplied by a scale factor, and the new rectangle has an area of 144 sq in. What was the scale factor?

\begin{equation}4x^{2}=144\end{equation}