Models and Solve Equations with Variables on Both Sides

Select the situation that could be modeled by: 120 + 25x = 45x.

• John bought a car radio for $120 and speakers for $25 each. Joe bought a radio for $45. They each paid the same. How much did they spend?

• George charges a flat fee of $120 to mow a lawn plus $25 an hour. Greg charges $45 a hour to mow a lawn. After how many hours do they make the same amount?

• Lisa pays $120 for each purse she buys plus an additional $25 to have them personalized. Lauren pays $45 for each purse she buys. How many purses must they buy for the amount they spent to be the same?

Select the situation that could be modeled by: 8 + 4x = 12 + 3x.

• Winnie bought a family meal with 8 burgers and 4 fries. Wilson bought a family meal with 12 burgers and 3 fries. If they each paid the same amount, how much did they spend?

• Team A runs 8 drills that a 4 minutes each. Team B runs 12 drills that are 3 minutes each. Which team practices longer?

• The basketball team currently has 8 players and is growing by 4 players each month. The volleyball team has 12 players and is growing by 3 players each month. After how many months will they have the same number of players?

The school board is selling pizzas for
$7 each to raise money for new
uniforms. The supplier charges $100
plus $4 per pizza. How many pizzas
does the school board need to sell to
make a profit?
(HINT: Write the equation & then solve.)

• 33
  

• 100

• 15

At Gamestop you can buy a Xbox One for $150.00 and each game to go with it would cost $24.00. Or, you can buy a Playstation 4 for $180.00 and each game for $20.00. Write an equation to determine how many games would need to be purchased for the cost to be equal?

• 150x + 24 = 180 + 20x

• 150 + 24x = 180 + 20x

• 180 - 150 = 24 x + 20x

• 150 - 24x = 180 - 20x

You ride an express bus from the center of town to your street. You have two payment options. Option A is to buy a monthly pass and pay $0.80 per ride. Option B is to pay $2.30 per ride. A monthly pass costs $30. After how many rides will the total costs of the two options be the same?

• r=20 rides

• r=10 rides

• r=15 rides

• r=25 rides

You play basketball in your school’s indoor stadium. You have two payment options. Option A is to buy a membership card and pay $2 each time you go to the gym. Option B is to pay $4 each time you go. A membership card costs $20. After how many times will the cost of Option A be equal to the cost of Option B?

• t=5 times

• t=7 times

• t=10 times

• t=13 times

Taxi company A charges $8.00 to get into the cab and $0.75 per mile. Taxi company B charges $6.00 to get into a cab and $1.25 per mile. How many miles would the cost be the same for both companies?

• 2 miles

• 4 miles

• 0.50 mile

• -4 miles

Tags

CCSS.8.EE.C.8C

Joe’s Canoes charges an initial fee of $20 plus $4 an hour. Callie’s Canoes charges a flat rate of $14 an hour. Find the number of hours for which the total amount that both places charge would be the same.

• 3 hours

• 4 hours

• 1 hour

• 2 hours

Which inequality represents the following problem:
The Rug store installs carpet for $80 plus $9.50 per square yard of carpet. The Magic Carpet charges $120 for instillation and $7.50 per square yard of carpet. Find the number of square yards of carpet for The Rug Store charges more than The Magic Carpet.

• 80+9.50x > 120+7.50x

• 80+9.50x < 120+7.50x

• 80x+9.50 > 120x+7.50

• 80x+9.50 < 120x+7.50

Tags

CCSS.7.EE.B.4B

• -x - 4 = 2x + 2

• -x - 2 = 2x - 4

• -x + 2 = 2x - 4