Expressions & Equations Review

Writing Expressions

100

Each week, Stephen gets an allowance of $8 plus $3 for each chore he does. His younger sister, Jill, gets an allowance of $6 plus $2 per chore. Write an expression for how much their parents give Stephen and Jill each week if they do the same number of chores.

14 +5c

200

A company sets up a food booth and a game booth at the county fair. The fee for the food booth is $100 plus $5 per day. The fee for the game booth is $50 plus $7 per day.

Write an expression for how much both booths will cost for the same number of days.

100+5d+50+7d or 150+12d

300

A group of 5 people go out to eat and buy appetizers and main dishes. They decide to split the bill so each person pays 20% of the total cost. Appetizers are $5 and main dishes are $10. Write an expression that shows how much each person pays.

0.2(5a + 10m) or a+2m

400

A basketball court has a length of 3x-14 and a width of 1/2x+32. Write an expression for the perimeter of the basketball court.

7x+36

500

A rectangle with a length of x+5 has a perimeter of 4x+14.

Write and simplify an expression for the width of the rectangle in terms of x.

x+2

Combining Like Terms

100

Simplify 8(5x-3y).

40x-24y

200

(3x+1/2)+(7x-4 1/2)

10x-4

300

Simplify (-0.75x+6)-(2.5x-1.9).

-3.25x+7.9

400

Simplify (36x+14)-[-2(6x-4)].

48x+6

500

Simplify (x+3)(x+2).

x^2+5x+6

Factoring Expressions

100

Factor 4x+20.

4(x+5)

200

Factor 6x-54.

6(x-9)

300

Factor -2.4x-3.2.

-0.8(3x+4)

400

Factor 27-9x+15y.

3(9-3x+5y)

500

Factor -72.5x-46y+63.5

-5(14.5x+9.2y-12.7)

Writing Equations

100

A scuba diver is exploring at an elevation of -12.2 meters. As the driver rises to the surface, she plans to stop and rest briefly at a reef that has an elevation of -4.55 meters. Write an equation to find the vertical distance that the diver traveled.

-12.2+x=-4.55

200

After a power failure, the temperature in a freezer increased at an average rate of 2.5 degrees per hour. The total increase was 7.5 degrees. Write an equation to find the number of hours until the power was restored.

2.5x=7.5

300

Between the hours of 10 p.m. and 6 a.m. the temperature decreases an average of 3/4 of a degree per hour. Write an equation for how many hours it will take for the temperature to decrease by 5 degrees.

-3/4x=-5

400

The value a share of stock decreases in value at a rate of $1.20 per hour during the first 3.5 hours of trading. Write an equation to find the decrease in the value of the share of stock during that time.

x/3.5=-1.2

500

A school bought$548 in basketball equipment and uniforms costing $29.50 each. The total cost was $2,023. Write an equation you can use to find the number of uniforms the school purchased.

29.5u+548=2,023

Solving Equations

100

Solve for n.

4.9+n=-9

n=-13.9

200

Solve for c.

7(c-12)=-21

c=9

300

Solve for b.

-17+b/8=13

b=240

400

Solve for k.

k/5.2+81.9=47.2

k=-180.44

500

Solve for d.

2/3d+8=48

d=60