Algebra-1 Problems

3.4 Phrases to Algebraic Expressions


Problem #

Problem Statement

Problems Similar To

1.

Write the expression for: 7 times a number, plus 4

\begin{equation}7x+4\end{equation}

2.

Write the expression for: 2 less than 7 times a number

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

3.

Write the expression for: 9 less than 1/2 of a number (enter answer in whole fractions)

\begin{equation}\frac{x}{2}-9\end{equation}

4.

This week Candice worked 7 hours more than 8 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}8x+7\end{equation}

5.

The depth of the new well is 10 ft less than 4 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}4x-10\end{equation}

6.

A case of 3 boxes of cereal costs $\$66$. There is also a shipping cost per case. The total cost for each box of cereal is $\$24$. What is the shipping cost per case?

\begin{equation}\frac{x+66}{3}=24\end{equation}

7.

A rectangular garden is 31 ft longer than it is wide. The total length of the fence that surrounds the garden is 82 ft. How wide is the garden?

\begin{equation}2(x+x+31)=82\end{equation}

8.

On a committee of 18 persons, there were 8 more women than men. How many men were on the committee?

\begin{equation}x+x+8=18\end{equation}

9.

Your friend rented a truck for $\$15$ per hour and a dolly for $\$5$ per hour. He paid a total of $\$80$ for the rental. How long did your friend rent the truck?

\begin{equation}x \times 15+x \times 5=80\end{equation}

10.

The membership fee for joining a gardening association is $\$78$ per year. A local botanical garden charges members of the gardening association $\$5$ for admission to the garden. Non-members of the association are charged $\$49/2$. 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}78+5x=\frac{49}{2} \times x\end{equation}

11.

The sum of two angles is 117 degrees. One angle is (2*x - 2) degrees and the other angle is 5*x degrees. Write and solve an equation to find "x".

\begin{equation}2x-2+5x=117\end{equation}

12.

For her cellular phone service, Samantha pays $\$61$ per month, plus $\$2$ for each hour over the allowed hours of the plan. Samantha received a bill for $\$95$ last month. For how many hours did she use her phone beyond the allowed hours?

\begin{equation}61+2x=95\end{equation}

13.

Jane has job offers at two companies. One company offers a starting salary of $\$71700$ with a raise of $\$2800$ each year. The other company offers a starting salary of $\$53200$ with a raise of $\$6500$ each year. After how many years would Jane's salary be the same with both companies?

\begin{equation}2800x+71700=6500x+53200\end{equation}

14.

You and 6 of your friends are going to race go-carts. The last time you went, you had a coupon for $\$2$ off each admission and paid a total of $\$84$ for everyone. This time you pay the regular price, how much does each person pay?

\begin{equation}(6+1)(x-2)=84\end{equation}

15.

When Tiffany's 1st CD sold a million copies, her record label gave her a $\$174000$ 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=174000\end{equation}

16.

A contractor needs to cut a piece of glass to fit a square window. The area of the window is 36 sq ft, find the length of the side of the window.

\begin{equation}x^{2}=36\end{equation}

17.

The number of chaperons at a school field trip must be 1/7 times the number of students attending, plus the 9 teacher sponsors. How many chaperons must be on the trip if there are 47 students?

\begin{equation}\frac{47}{7}+9=x\end{equation}