Name ____________________________

Unit 5 Final Assessment

Define the variables and translate the following expressions into equations or inequalities.

1. a. Peter’s Lawn Mowing Service charges $10 per job and $0.20 per square yard. Peter earns $25 for a job.

    b. Renting the ice-skating rink for a birthday party costs $200 plus $4 per person. The rental costs $324 in total.

    c. A bus can seat 65 passengers or fewer.

    d. You buy hamburgers at a fast food restaurant. A hamburger costs $0.49. You have at most $3 to spend.

Check that the given number is a solution to the corresponding equation or inequality.

2. a. y =2; 2.5y - 10.0 = -5.0

     b. z = -5; 2(5 - 2z) = 20 - 2 (z - 1)

     c. y = 40; - \frac{5} {2}y + \frac{1} {2} < -18

     d. t = 0.4; 80 \ge 10(3t + 2)

Write an algebraic expression for each situation below.

3. Arturo has eight fewer stickers in his collection than Julissa has in hers. Let jrepresent the number of stickers in Julissa's collection. Write an expression to represent the number of stickers in Arturo's collection.

Solve each single-variable equation.

4. a. x+30=47

    b. b-13=50

    c. -1.4x=2.8

    d. \frac{b}{8}=-10

5. Christina has 40 coins in her collection. She has 21 fewer coins in her collection than Shaya has in hers.

a. Write an equation to represent s, the number of coins in Shaya's collection.

b. Determine how many coins are in Shaya's collection.

6. Mrs. Kowalski divided the students in the seventh grade into seven equal-sized groups. There were 25 students in each group.

a. Write an equation to represent s, the total number of students in the seventh grade.

b. Determine the total number of students in the seventh grade.

7. Write the following two-step equations from verbal models.

a.Two times a number, plus seven, is nineteen.

b. Three times a number, plus five, is twenty.

8. Solve each two-step equation for the unknown variable.

a. 3x+2=14

b. 6y+5=29

Write an expression and/or solve each problem.

9. Augusta sells t-shirts at the school store. On Tuesday, Augusta sold seven less than twice the number of t-shirts she sold on Monday. She sold three t-shirts on Tuesday. Write an algebraic equation to represent m, the number of t-shirts August sold on Monday.

10. For each babysitting job he takes on, Manuel charges $2 for bus fare plus an additional $6 for each hour he works at the job. On Saturday, Manuel earned $26 for one babysitting job.

a. Write an equation to represent h, the total number of hours that Manuel babysat during his $26 job.

b. Determine the total number of hours that Manuel babysat during that job.