Algebra-1 Problems

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1.

Solve for x

\begin{equation}\frac{x}{10}=\frac{\frac{24}{5}}{6}\end{equation}

2.

Solve for x

\begin{equation}\frac{x}{20}=\frac{1}{5}\end{equation}

3.

Solve for x

\begin{equation}\frac{\frac{5}{3}}{10}=\frac{1}{x}\end{equation}

4.

Solve for x

\begin{equation}\frac{\frac{90}{7}}{2}=\frac{9x}{7}\end{equation}

5.

Solve for x

\begin{equation}\frac{\frac{21}{5}}{x}=\frac{6}{x+3}\end{equation}

6.

Solve for x

\begin{equation}\frac{1}{\frac{3}{2}}=\frac{x}{x+2}\end{equation}

7.

Solve for x

\begin{equation}\frac{4-x}{2}=\frac{4}{-4}\end{equation}

8.

Solve for x

\begin{equation}\frac{x}{35}=\frac{\frac{2}{10}}{\frac{7}{10}}\end{equation}

9.

Solve for x

\begin{equation}\frac{x}{\frac{16}{5}}=\frac{\frac{10}{10}}{\frac{4}{10}}\end{equation}

10.

If a car moving at constant speed travels 181 miles in 2 hours, how many miles will it travel in 7 hours?

\begin{equation}\frac{181}{2}=\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 8 seconds. How many pieces of mail should you be able to sort in 9 minutes?

\begin{equation}\frac{10}{8}=\frac{x}{9 \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 26/17 inches tall.

\begin{equation}\frac{1}{17}=\frac{\frac{26}{17}}{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 36 miles. On the map, how many centimeters are between the two Cities?

\begin{equation}\frac{1}{9}=\frac{x}{36}\end{equation}

14.

The utility worker is 5 ft tall and is casting a shadow 9 ft long. At the same time, a nearby utility pole casts a shadow 27/5 ft long. Write and solve a proportion to find the height of the utility pole.

\begin{equation}\frac{5}{9}=\frac{x}{\frac{27}{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 567 sq in. What was the scale factor?

\begin{equation}7x^{2}=567\end{equation}