Algebra-1 Problems

3.4 Phrases to Algebraic Expressions


Problem #

Problem Statement

Problems Similar To

1.

Write the expression for: 4 times a number, plus 8

\begin{equation}4x+8\end{equation}

2.

Write the expression for: 4 less than 9 times a number

\begin{equation}9x-4\end{equation}

3.

Write the expression for: 7 less than 1/4 of a number (enter answer in whole fractions)

\begin{equation}\frac{x}{4}-7\end{equation}

4.

This week Candice worked 2 hours more than 7 times as many hours as last week. Let "x" be the hours worked last week. Write an expression for the hours worked this week.

\begin{equation}7x+2\end{equation}

5.

The depth of the new well is 3 ft less than 6 times the depth of the old well. Let "x" be the depth of the old well. Write an expression for the depth of the new well.

\begin{equation}6x-3\end{equation}

6.

A case of 6 boxes of cereal costs $\$84$. There is also a shipping cost per case. The total cost for each box of cereal is $\$89/6$. What is the shipping cost per case?

\begin{equation}\frac{x+84}{6}=\frac{89}{6}\end{equation}

7.

A rectangular garden is 39 ft longer than it is wide. The total length of the fence that surrounds the garden is 106 ft. How wide is the garden?

\begin{equation}2(x+x+39)=106\end{equation}

8.

On a committee of 13 persons, there were 7 more women than men. How many men were on the committee?

\begin{equation}x+x+7=13\end{equation}

9.

Your friend rented a truck for $\$19$ per hour and a dolly for $\$4$ per hour. He paid a total of $\$138$ for the rental. How long did your friend rent the truck?

\begin{equation}x \times 19+x \times 4=138\end{equation}

10.

The membership fee for joining a gardening association is $\$81$ per year. A local botanical garden charges members of the gardening association $\$4$ for admission to the garden. Non-members of the association are charged $\$31$. After how many visits to the garden is the total cost for the members, including membership fee, same as total cost for non-members?

\begin{equation}81+4x=31x\end{equation}

11.

The sum of two angles is 135 degrees. One angle is (5*x - 5) degrees and the other angle is 5*x degrees. Write and solve an equation to find "x".

\begin{equation}5x-5+5x=135\end{equation}

12.

For her cellular phone service, Samantha pays $\$57$ per month, plus $\$2$ for each hour over the allowed hours of the plan. Samantha received a bill for $\$93$ last month. For how many hours did she use her phone beyond the allowed hours?

\begin{equation}57+2x=93\end{equation}

13.

Jane has job offers at two companies. One company offers a starting salary of $\$71600$ with a raise of $\$4800$ each year. The other company offers a starting salary of $\$57100$ with a raise of $\$7700$ each year. After how many years would Jane's salary be the same with both companies?

\begin{equation}4800x+71600=7700x+57100\end{equation}

14.

You and 8 of your friends are going to race go-carts. The last time you went, you had a coupon for $\$4$ off each admission and paid a total of $\$90$ for everyone. This time you pay the regular price, how much does each person pay?

\begin{equation}(8+1)(x-4)=90\end{equation}

15.

When Tiffany's 1st CD sold a million copies, her record label gave her a $\$199200$ bonus. She split the money evenly between herself, her agent, her producer and her stylist. How much money did each person receive?

\begin{equation}4x=199200\end{equation}

16.

A contractor needs to cut a piece of glass to fit a square window. The area of the window is 49 sq ft, find the length of the side of the window.

\begin{equation}x^{2}=49\end{equation}

17.

The number of chaperons at a school field trip must be 1/3 times the number of students attending, plus the 4 teacher sponsors. How many chaperons must be on the trip if there are 97 students?

\begin{equation}\frac{97}{3}+4=x\end{equation}