Algebra-1 Problems

3.4 Phrases to Algebraic Expressions


Problem #

Problem Statement

Problems Similar To

1.

Write the expression for: 6 times a number, plus 4

\begin{equation}6x+4\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: 6 less than 1/8 of a number (enter answer in whole fractions)

\begin{equation}\frac{x}{8}-6\end{equation}

4.

This week Candice worked 8 hours more than 10 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}10x+8\end{equation}

5.

The depth of the new well is 7 ft less than 10 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}10x-7\end{equation}

6.

A case of 9 boxes of cereal costs $\$86$. There is also a shipping cost per case. The total cost for each box of cereal is $\$10$. What is the shipping cost per case?

\begin{equation}\frac{x+86}{9}=10\end{equation}

7.

A rectangular garden is 33 ft longer than it is wide. The total length of the fence that surrounds the garden is 102 ft. How wide is the garden?

\begin{equation}2(x+x+33)=102\end{equation}

8.

On a committee of 11 persons, there were 5 more women than men. How many men were on the committee?

\begin{equation}x+x+5=11\end{equation}

9.

Your friend rented a truck for $\$22$ per hour and a dolly for $\$6$ per hour. He paid a total of $\$84$ for the rental. How long did your friend rent the truck?

\begin{equation}x \times 22+x \times 6=84\end{equation}

10.

The membership fee for joining a gardening association is $\$64$ per year. A local botanical garden charges members of the gardening association $\$2$ for admission to the garden. Non-members of the association are charged $\$42/5$. 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}64+2x=\frac{42}{5} \times x\end{equation}

11.

The sum of two angles is 135 degrees. One angle is (6*x - 8) degrees and the other angle is 7*x degrees. Write and solve an equation to find "x".

\begin{equation}6x-8+7x=135\end{equation}

12.

For her cellular phone service, Samantha pays $\$87$ per month, plus $\$2$ for each hour over the allowed hours of the plan. Samantha received a bill for $\$111$ last month. For how many hours did she use her phone beyond the allowed hours?

\begin{equation}87+2x=111\end{equation}

13.

Jane has job offers at two companies. One company offers a starting salary of $\$54428$ with a raise of $\$3800$ each year. The other company offers a starting salary of $\$49600$ with a raise of $\$5007$ each year. After how many years would Jane's salary be the same with both companies?

\begin{equation}3800x+54428=5007x+49600\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 $\$81$ for everyone. This time you pay the regular price, how much does each person pay?

\begin{equation}(8+1)(x-4)=81\end{equation}

15.

When Tiffany's 1st CD sold a million copies, her record label gave her a $\$152800$ 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=152800\end{equation}

16.

A contractor needs to cut a piece of glass to fit a square window. The area of the window is 16 sq ft, find the length of the side of the window.

\begin{equation}x^{2}=16\end{equation}

17.

The number of chaperons at a school field trip must be 1/3 times the number of students attending, plus the 2 teacher sponsors. How many chaperons must be on the trip if there are 58 students?

\begin{equation}\frac{58}{3}+2=x\end{equation}