### 3.4 Phrases to Algebraic Expressions

Problem #

Problem Statement

Problems Similar To

1.

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

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

2.

Write the expression for: 5 less than 2 times a number

\begin{equation}2x-5\end{equation}

3.

Write the expression for: 7 less than 1/6 of a number (enter answer in whole fractions)

\begin{equation}\frac{x}{6}-7\end{equation}

4.

This week Candice worked 7 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+7\end{equation}

5.

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

6.

A case of 10 boxes of cereal costs $\$61$. There is also a shipping cost per case. The total cost for each box of cereal is$\$7$. What is the shipping cost per case?

\begin{equation}\frac{x+61}{10}=7\end{equation}

7.

A rectangular garden is 28 ft longer than it is wide. The total length of the fence that surrounds the garden is 72 ft. How wide is the garden?

\begin{equation}2(x+x+28)=72\end{equation}

8.

On a committee of 15 persons, there were 9 more women than men. How many men were on the committee?

\begin{equation}x+x+9=15\end{equation}

9.

Your friend rented a truck for $\$22$per hour and a dolly for$\$5$ per hour. He paid a total of $\$81$for the rental. How long did your friend rent the truck? \begin{equation}x \times 22+x \times 5=81\end{equation} 10. The membership fee for joining a gardening association is$\$69$ 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$\$99/10$. 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}69+3x=\frac{99}{10} \times x\end{equation}

11.

The sum of two angles is 129 degrees. One angle is (7*x - 3) degrees and the other angle is 4*x degrees. Write and solve an equation to find "x".

\begin{equation}7x-3+4x=129\end{equation}

12.

For her cellular phone service, Samantha pays $\$74$per month, plus$\$2$ for each hour over the allowed hours of the plan. Samantha received a bill for $\$108$last month. For how many hours did she use her phone beyond the allowed hours? \begin{equation}74+2x=108\end{equation} 13. Jane has job offers at two companies. One company offers a starting salary of$\$105500$ with a raise of $\$1900$each year. The other company offers a starting salary of$\$50600$ with a raise of $\$8000$each year. After how many years would Jane's salary be the same with both companies? \begin{equation}1900x+105500=8000x+50600\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 $\$70$for everyone. This time you pay the regular price, how much does each person pay? \begin{equation}(6+1)(x-3)=70\end{equation} 15. When Tiffany's 1st CD sold a million copies, her record label gave her a$\$198300$ 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=198300\end{equation}

16.

A contractor needs to cut a piece of glass to fit a square window. The area of the window is 25 sq ft, find the length of the side of the window.

\begin{equation}x^{2}=25\end{equation}

17.

The number of chaperons at a school field trip must be 1/6 times the number of students attending, plus the 6 teacher sponsors. How many chaperons must be on the trip if there are 73 students?

\begin{equation}\frac{73}{6}+6=x\end{equation}