Simplifying Expressions
Simplify the following expression:
3x + 9x
12x
Solve for a:
4a + 3 = 11
a = 2
Paul bought a student discount card for the bus. The card cost $7 and allows him to buy daily bus passes for $1.50. After one month, Paul spent $29.50. Write an equation to represent this situation. Double points if you also solve.
7 + 1.50p=29.50
p=15
Solve for x: 7x - 1 = 4x + 5
x = 2
Jack and Jessica earned the same amount last week. They both make the same amount per hour. Jack worked eighteen hours and had $42 deducted from his pay. Jessica worked fifteen hours and had $18 deducted from her pay. Write an equation to represent this situation. Double points to solve. What was each person’s salary last week after deductions?
18x - 42 = 15x -18
Each earned $102 after deductions.
Jennifer is saving money to buy a bike. The bike costs $245. She has $125 saved, and each week she adds $15 to her savings.Write an equation to represent this situation. Double points to solve. How long will it take her to save enough money to buy the bike?
125+15w=245
It will take 8 weeks for Jennifer to save up for the bike.
Solve for w:
2w + 3 = 4w - 5
w = 4
Joshua can purchase tile at one store for $0.99 per tile, but he will have to rent a tile saw for $25. At another store he can buy tile for $1.50 per tile and borrow a tile saw for free.Write an equation to represent this situation. Double points to solve. Find the number of tiles for which the cost is the same. Round to the nearest tile.
.99x+25=1.50x
For 49 tiles the cost will be the same for both companies.
Solve for x:
28 = 8x + 12 - 7x
x = 16
Together Marc and Paoli have $32. Marc has $4 less than twice the amount Paoli has. Write an equation to represent this situation. Double points to solve. How much does each man have?
P + 2P-4=32
Marc has 20 dollars and Paoli has 12 dollars.
Solve for y:
15y + 14 = 2(5y + 6)
y = -0.4 or -2/5
One plumber charges a fee of $75 per service call plus $15 per hour. Another plumber has no flat fee, but charges $25 per hour.Write an equation to represent this situation. Double points to solve. Find the number of hours for which the cost of the two plumbers is the same.
75+15h=25h
For 7.5 hours of work, both companies will charge the same amount.
Simplify the following expression:
8x + 2x - 3y - 9x
x - 3y
Two angles are complementary. One angle is 28 degrees more than the other one. Write an equation to represent this situation. Double points to solve. Find the measure of each angle.
x + x+28 = 90
Angle 1 = 31 degrees Angle 2 = 59 degrees
Solve for d:
4(3d - 2) = 8d - 5
d = 0.75 or d=3/4
Carpet Plus installs carpet for $100 plus $8 per square yard of carpet. Carpet World charges $75 for installation and $10 per square yard of carpet.Write an equation to represent this situation. Double points to solve. Find the number of square yards of carpet for which the cost including carpet and installation is the same.
100 + 8x = 75 + 10x
12.5 square yards of carpeting will cost the same for both companies.
A triangle has side lengths of
4p, 8 - p, and 3p + 1.
Write an expression for the perimeter of the triangle.
6p + 9
Solve for p:
17 = 3(p - 5) + 8
p = 8
Takeo drove to a baseball game. His ticket cost $10.50 and parking was $6. Takeo bought two boxes of popcorn that cost $2.25 a box. Takeo also bought 1 drink. The baseball game and the snacks cost a total of $24.50.Write an equation to represent this situation. Double points to solve. How much did his drink cost?
10.50 + 6 + 2(2.25) +d =24.50
His drink cost $3.50
Solve for a:
5(5a +3) = 14a - 29
a = -4
Fifteen more than twice the hours Carla worked last week is the same as three times the hours she worked this week decreased by 15. She worked the same number of hours each week. How many hours did she work each week?
15 + 2h = 3h - 15
She worked for 30 hours both weeks.