Writing, Modeling, and Solving Equations with Variables

A rental car agency charges $30.00 per day plus per mile $0.15. Another rental car agency charges $36.00 per day plus $0.10 per mile. Which equation could be used to determine how many miles would have to be driven in one day for both rental agencies to cost the same amount to rent? 

• 30 + 0.15x = 36 + 0.10x
• 30 - 0.15x = 36 - 0.10x
• 30 + 36 = 0.10x + 0.36x
• 36 - 30 = 0.36x + 0.10x

Tags

CCSS.6.EE.A.4

CCSS.6.EE.B.5

CCSS.6.EE.B.6

CCSS.6.EE.B.7

CCSS.6.EE.C.9

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 

Tags

CCSS.8.EE.C.8C

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

Tags

CCSS.6.EE.B.6

CCSS.6.EE.B.7

CCSS.6.EE.C.9

Mary has been offered two jobs. Job A has a starting salary of $36,000 and a raise of $1500 every year. Job B has a starting salary of $29,000 and a raise of $2500 every year. Write an equation to determine how many years would Mary's salary be the same at both companies. 

• 36,000x + 1,500 = 29,000x + 2,500
• 36,000 - 29,000 = 1,500x + 2,500x
• 36,000 - 1,500x = 29,000 - 2,500x
• 36,000 + 1,500x = 29,000 + 2,500x

Tags

CCSS.6.EE.A.4

CCSS.6.EE.B.6

CCSS.6.EE.B.7

CCSS.6.EE.C.9

What inequality symbol is used in:
384 + 2x < 6x?

• Greater Than
• Less Than
• Greater Than or Equal To
• Less Than or Equal To

The Rug store installs carpet for $80 plus $9.50 per square yard of carpet. The Magic Carpet charges $120 for installation and $7.50 per square yard of carpet. Write an inequality that could be used to determine the number of square yards of carpet that need to be installed for The Rug Store to charge 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

Cody’s Gym charges a $15 fee to join and $30 per month. Tyler’s Gym charges a $30 fee to join and $20 per month. Write an inequality that could be used to determine after how many months Tyler’s gym would be a better deal.

• 30 + 20x < 15 + 30x
• 30x + 20 < 15x + 30
• 30 + 20x > 15 + 30x
• 30x + 20 > 15x + 30

• 2

• 4

• 0.5

• 8

What value of m makes this equation true?

• m = -3 
• m = 3
• m = 4
• m = 2

What value of m makes this equation true?

• m = -3 
• m = 3
• m = 4
• m = 2