### 3.4 Phrases to Algebraic Expressions

Problem #

Problem Statement

Problems Similar To

1.

Write the expression for: 7 times a number, plus 10

$$7x+10$$

2.

Write the expression for: 2 less than 10 times a number

$$10x-2$$

3.

Write the expression for: 10 less than 1/5 of a number (enter answer in whole fractions)

$$\frac{x}{5}-10$$

4.

This week Candice worked 5 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.

$$10x+5$$

5.

The depth of the new well is 3 ft less than 9 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.

$$9x-3$$

6.

A case of 10 boxes of cereal costs $\$59$. There is also a shipping cost per case. The total cost for each box of cereal is$\$69/10$. What is the shipping cost per case?

$$\frac{x+59}{10}=\frac{69}{10}$$

7.

A rectangular garden is 44 ft longer than it is wide. The total length of the fence that surrounds the garden is 128 ft. How wide is the garden?

$$2(x+x+44)=128$$

8.

On a committee of 27 persons, there were 9 more women than men. How many men were on the committee?

$$x+x+9=27$$

9.

Your friend rented a truck for $\$15$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? $$x \times 15+x \times 6=84$$ 10. The membership fee for joining a gardening association is$\$98$ 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$\$89/4$. After how many visits to the garden is the total cost for the members, including membership fee, same as total cost for non-members?

$$98+10x=\frac{89}{4} \times x$$

11.

The sum of two angles is 96 degrees. One angle is (2*x - 6) degrees and the other angle is 4*x degrees. Write and solve an equation to find "x".

$$2x-6+4x=96$$

12.

For her cellular phone service, Samantha pays $\$75$per month, plus$\$2$ for each hour over the allowed hours of the plan. Samantha received a bill for $\$109$last month. For how many hours did she use her phone beyond the allowed hours? $$75+2x=109$$ 13. Jane has job offers at two companies. One company offers a starting salary of$\$91400$ with a raise of $\$1200$each year. The other company offers a starting salary of$\$52400$ with a raise of $\$7700$each year. After how many years would Jane's salary be the same with both companies? $$1200x+91400=7700x+52400$$ 14. You and 9 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 $\$100$for everyone. This time you pay the regular price, how much does each person pay? $$(9+1)(x-3)=100$$ 15. When Tiffany's 1st CD sold a million copies, her record label gave her a$\$177500$ bonus. She split the money evenly between herself, her agent, her producer and her stylist. How much money did each person receive?

$$4x=177500$$

16.

A contractor needs to cut a piece of glass to fit a square window. The area of the window is 81 sq ft, find the length of the side of the window.

$$x^{2}=81$$

17.

The number of chaperons at a school field trip must be 1/10 times the number of students attending, plus the 2 teacher sponsors. How many chaperons must be on the trip if there are 82 students?

$$\frac{82}{10}+2=x$$