Algebra-1 Problems

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1.

Solve for x

\begin{equation}\frac{x}{4}=\frac{14}{8}\end{equation}

2.

Solve for x

\begin{equation}\frac{x}{35}=\frac{1}{5}\end{equation}

3.

Solve for x

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

4.

Solve for x

\begin{equation}\frac{\frac{189}{10}}{3}=\frac{7x}{10}\end{equation}

5.

Solve for x

\begin{equation}\frac{\frac{20}{3}}{x}=\frac{10}{x+2}\end{equation}

6.

Solve for x

\begin{equation}\frac{1}{\frac{13}{10}}=\frac{x}{x+3}\end{equation}

7.

Solve for x

\begin{equation}\frac{8-x}{4}=\frac{8}{\frac{32}{5}}\end{equation}

8.

Solve for x

\begin{equation}\frac{x}{\frac{7}{3}}=\frac{\frac{9}{10}}{\frac{3}{10}}\end{equation}

9.

Solve for x

\begin{equation}\frac{x}{\frac{27}{8}}=\frac{\frac{8}{10}}{\frac{9}{10}}\end{equation}

10.

If a car moving at constant speed travels 197 miles in 1 hours, how many miles will it travel in 9 hours?

\begin{equation}\frac{197}{1}=\frac{x}{9}\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 8 pieces of mail in 15 seconds. How many pieces of mail should you be able to sort in 2 minutes?

\begin{equation}\frac{8}{15}=\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 : 13 ft. Estimate the height of the building whose model is 32/13 inches tall.

\begin{equation}\frac{1}{13}=\frac{\frac{32}{13}}{x}\end{equation}

13.

The scale of a map of State X shows that 1 cm represents 14 miles. The actual distance from City A to City B is 126 miles. On the map, how many centimeters are between the two Cities?

\begin{equation}\frac{1}{14}=\frac{x}{126}\end{equation}

14.

The utility worker is 7 ft tall and is casting a shadow 9 ft long. At the same time, a nearby utility pole casts a shadow 90/7 ft long. Write and solve a proportion to find the height of the utility pole.

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

15.

A rectangle has an area of 5 sq in. Every dimension of the rectangle is multiplied by a scale factor, and the new rectangle has an area of 405 sq in. What was the scale factor?

\begin{equation}5x^{2}=405\end{equation}