### 3.4 Phrases to Algebraic Expressions

Problem #

Problem Statement

Problems Similar To

1.

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

$$5x+8$$

2.

Write the expression for: 4 less than 5 times a number

$$5x-4$$

3.

Write the expression for: 7 less than 1/8 of a number (enter answer in whole fractions)

$$\frac{x}{8}-7$$

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.

$$10x+7$$

5.

The depth of the new well is 7 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.

$$6x-7$$

6.

A case of 3 boxes of cereal costs $\$96$. There is also a shipping cost per case. The total cost for each box of cereal is$\$33$. What is the shipping cost per case?

$$\frac{x+96}{3}=33$$

7.

A rectangular garden is 47 ft longer than it is wide. The total length of the fence that surrounds the garden is 102 ft. How wide is the garden?

$$2(x+x+47)=102$$

8.

On a committee of 12 persons, there were 4 more women than men. How many men were on the committee?

$$x+x+4=12$$

9.

Your friend rented a truck for $\$17$per hour and a dolly for$\$6$ per hour. He paid a total of $\$138$for the rental. How long did your friend rent the truck? $$x \times 17+x \times 6=138$$ 10. The membership fee for joining a gardening association is$\$62$ per year. A local botanical garden charges members of the gardening association $\$10$for admission to the garden. Non-members of the association are charged$\$71/4$. After how many visits to the garden is the total cost for the members, including membership fee, same as total cost for non-members?

$$62+10x=\frac{71}{4} \times x$$

11.

The sum of two angles is 287 degrees. One angle is (7*x - 7) degrees and the other angle is 7*x degrees. Write and solve an equation to find "x".

$$7x-7+7x=287$$

12.

For her cellular phone service, Samantha pays $\$53$per month, plus$\$2$ for each hour over the allowed hours of the plan. Samantha received a bill for $\$81$last month. For how many hours did she use her phone beyond the allowed hours? $$53+2x=81$$ 13. Jane has job offers at two companies. One company offers a starting salary of$\$86200$ with a raise of $\$2800$each year. The other company offers a starting salary of$\$49800$ with a raise of $\$8000$each year. After how many years would Jane's salary be the same with both companies? $$2800x+86200=8000x+49800$$ 14. You and 7 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 $\$96$for everyone. This time you pay the regular price, how much does each person pay? $$(7+1)(x-2)=96$$ 15. When Tiffany's 1st CD sold a million copies, her record label gave her a$\$183000$ bonus. She split the money evenly between herself, her agent, her producer and her stylist. How much money did each person receive?

$$4x=183000$$

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.

$$x^{2}=16$$

17.

The number of chaperons at a school field trip must be 1/5 times the number of students attending, plus the 3 teacher sponsors. How many chaperons must be on the trip if there are 92 students?

$$\frac{92}{5}+3=x$$