Model With Equations

Greens are positive and reds are negative. Solve for x.

• x + 9 = -8

• -x + 9 = -8

• x - 9 = -8

• x + 9 = 8

The table shows the enrollment in a course over time since 1980.

Write and equation that models this data.

Your responses will have two digits behind the decimals.

Mathematical Equivalence

ON

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

The Frederick County Fair costs $15.00 to get in and $2.50 per ride, while the Montgomery County Fair costs $10.00 to get in and $3.00 per ride. Which equations could be used to determine how many rides you would need to go on for both fairs to be of equal value? 

• 15x + 2.5 = 10x + 3

• 15 - 2.5x = 10 - 3x

• 15 + 2.5x = 10 + 3x

• 15 - 10 = 2.5x + 3x

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

• .50 mile

• -4 miles

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

Peppy Pets charges a flat fee of $15 plus $3 per hour to keep a dog during the day. Happy Hounds charges a flat fee of $21 plus $1 per hour. For how many hours is the total fee charged by the companies the same?

• 2 hours

• 3 hours

• 4 hours

• 5 hours