### 3.4 Phrases to Algebraic Expressions

Problem #

Problem Statement

Problems Similar To

1.

Write the expression for: 2 times a number, plus 6

\begin{equation}2x+6\end{equation}

2.

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

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

3.

Write the expression for: 6 less than 1/9 of a number (enter answer in whole fractions)

\begin{equation}\frac{x}{9}-6\end{equation}

4.

This week Candice worked 4 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+4\end{equation}

5.

The depth of the new well is 6 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-6\end{equation}

6.

A case of 3 boxes of cereal costs $\$60$. There is also a shipping cost per case. The total cost for each box of cereal is$\$65/3$. What is the shipping cost per case?

\begin{equation}\frac{x+60}{3}=\frac{65}{3}\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 24 persons, there were 4 more women than men. How many men were on the committee?

\begin{equation}x+x+4=24\end{equation}

9.

Your friend rented a truck for $\$12$per hour and a dolly for$\$6$ per hour. He paid a total of $\$90$for the rental. How long did your friend rent the truck? \begin{equation}x \times 12+x \times 6=90\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 $\$5$for admission to the garden. Non-members of the association are charged$\$67/3$. 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+5x=\frac{67}{3} \times x\end{equation}

11.

The sum of two angles is 223 degrees. One angle is (6*x - 7) degrees and the other angle is 4*x degrees. Write and solve an equation to find "x".

\begin{equation}6x-7+4x=223\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 $\$91$last month. For how many hours did she use her phone beyond the allowed hours? \begin{equation}57+2x=91\end{equation} 13. Jane has job offers at two companies. One company offers a starting salary of$\$99600$ with a raise of $\$2800$each year. The other company offers a starting salary of$\$51600$ with a raise of $\$7600$each year. After how many years would Jane's salary be the same with both companies? \begin{equation}2800x+99600=7600x+51600\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$\$3$ 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}(6+1)(x-3)=56\end{equation} 15. When Tiffany's 1st CD sold a million copies, her record label gave her a$\$169800$ 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=169800\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 9 teacher sponsors. How many chaperons must be on the trip if there are 19 students?

\begin{equation}\frac{19}{3}+9=x\end{equation}