Algebra-1 Problems

3.4 Phrases to Algebraic Expressions


Problem #

Problem Statement

Problems Similar To

1.

Write the expression for: 8 times a number, plus 5

\begin{equation}8x+5\end{equation}

2.

Write the expression for: 10 less than 4 times a number

\begin{equation}4x-10\end{equation}

3.

Write the expression for: 3 less than 1/7 of a number (enter answer in whole fractions)

\begin{equation}\frac{x}{7}-3\end{equation}

4.

This week Candice worked 9 hours more than 9 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}9x+9\end{equation}

5.

The depth of the new well is 3 ft less than 5 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}5x-3\end{equation}

6.

A case of 11 boxes of cereal costs $\$92$. There is also a shipping cost per case. The total cost for each box of cereal is $\$9$. What is the shipping cost per case?

\begin{equation}\frac{x+92}{11}=9\end{equation}

7.

A rectangular garden is 38 ft longer than it is wide. The total length of the fence that surrounds the garden is 108 ft. How wide is the garden?

\begin{equation}2(x+x+38)=108\end{equation}

8.

On a committee of 17 persons, there were 3 more women than men. How many men were on the committee?

\begin{equation}x+x+3=17\end{equation}

9.

Your friend rented a truck for $\$16$ per hour and a dolly for $\$4$ per hour. He paid a total of $\$120$ for the rental. How long did your friend rent the truck?

\begin{equation}x \times 16+x \times 4=120\end{equation}

10.

The membership fee for joining a gardening association is $\$52$ per year. A local botanical garden charges members of the gardening association $\$3$ for admission to the garden. Non-members of the association are charged $\$35/3$. 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}52+3x=\frac{35}{3} \times x\end{equation}

11.

The sum of two angles is 228 degrees. One angle is (7*x - 6) degrees and the other angle is 6*x degrees. Write and solve an equation to find "x".

\begin{equation}7x-6+6x=228\end{equation}

12.

For her cellular phone service, Samantha pays $\$62$ per month, plus $\$2$ for each hour over the allowed hours of the plan. Samantha received a bill for $\$94$ last month. For how many hours did she use her phone beyond the allowed hours?

\begin{equation}62+2x=94\end{equation}

13.

Jane has job offers at two companies. One company offers a starting salary of $\$107600$ with a raise of $\$2800$ each year. The other company offers a starting salary of $\$57200$ with a raise of $\$8400$ each year. After how many years would Jane's salary be the same with both companies?

\begin{equation}2800x+107600=8400x+57200\end{equation}

14.

You and 7 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 $\$56$ for everyone. This time you pay the regular price, how much does each person pay?

\begin{equation}(7+1)(x-4)=56\end{equation}

15.

When Tiffany's 1st CD sold a million copies, her record label gave her a $\$172900$ 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=172900\end{equation}

16.

A contractor needs to cut a piece of glass to fit a square window. The area of the window is 64 sq ft, find the length of the side of the window.

\begin{equation}x^{2}=64\end{equation}

17.

The number of chaperons at a school field trip must be 1/9 times the number of students attending, plus the 7 teacher sponsors. How many chaperons must be on the trip if there are 69 students?

\begin{equation}\frac{69}{9}+7=x\end{equation}