Equations and Inequalities

Gym A charges a registration fee of $75 plus $35.75 per month for members. Gym B charges a registration fee of $164 plus $17.95  per month for members. Which equation best shows the number of months, m, it will take for the two gyms to charge the same amount?

• 75m + 35.75 = 164m + 17.95
• 75 + 35.75 = 164 + 17.95
• 75 + 35.75m = 164 + 17.95m
• 75m + 35.75m = 164m + 17.95m

Gym A charges a registration fee of $75 plus $35.75 per month for members. Gym B charges a registration fee of $164 plus $17.95  per month for members. After how many months would the total cost at Gym A and Gym B to be the same for members?

• 10 months
• 5 months
• 7 months
• The cost will never be the same

Tags

CCSS.8.EE.C.8C

The graph shows the number of hours that Rue and Zoe have been working at their jobs, as well as how much money they’ve earned. Which is a correct conclusion about the information shown in the graph?

• After 24 hours, Rue and Zoe will haveearned the same amount of money.
  
• After 4 hours, Zoe will have earned $12 more than Rue.
  
• After 4 hours, Rue will have earned $12 more than Zoe.
  
• After 4 hours, Rue and Zoe will have earned the same amount of money.
  

Tags

CCSS.8.EE.B.5

Barrett is ordering t-shirts for his school’s student council. Company D charges a $30 design fee plus $6.25 per t-shirt. Company E charges a $12 design fee plus $9.75 per t-shirt. Which inequality can be used to find x, the minimum number of t-shirts that can be ordered so that the total cost with Company D is less than the total cost with Company E?

• 6.25x + 30 > 9.75x + 12
• 6.25x + 30 < 9.75x + 12
• 6.25 + 30x > 9.75 + 12x
• 6.25 + 30x < 9.75 + 12x

Tags

CCSS.7.EE.B.4B

Identify the equation modeled below, and then find its solution.

• Equation: 4x + 4 = -x + 1; Solution: x = -0.6
• Equation: -4x + 4 = -x – 1; Solution: x = 1.6
• Equation: 4x – 4 = -x – 1; Solution: x = 0.6
• Equation: 4x – 4 = -x – 1; Solution: x = 1

Puppy A weighs 4 and 1/6 pounds at birth and gains 3/4 pound each week. Puppy B weighs 5 and 2/3 pounds at birth and gains 1/2 pound each week. Which equation shows the number of weeks, w, it will take for Puppy A to weigh the same amount as Puppy B?

• 4  1/6 + 3/4w = 5  2/3 + 1/2w
• 4  1/6w + 3/4 = 5  2/3w + 1/2
• 4  1/6w + 3/4w = 5  2/3 + 1/2
• 4  1/6 + 2/4 = 5  2/3w + 1/2w

Tags

CCSS.8.EE.C.7B

Solve for x:

• 6
• 12
• 2
• 7

Which of the following can be determined from the graph below?

• The ordered pair (6, 25) is a solution
• The ordered pair (25, 6) is a solution
• The ordered pair (6, 5) is a solution
• The ordered pair (5, 6) is a solution

Tags

CCSS.8.EE.C.8B

Which of the following situations could be solved by using the inequality shown below?

• Park A charges an entrance fee of $9 plus$1.25 per ride. Park B charges $14 perride and an entrance fee of $0.75. After how many rides will the total charge at Park A cost more than Park B?
  
• Danny finishes 1.25 homework problemsevery 9 minutes. Katie finishes 0.75homework problems every 14 minutes.After how many minutes will Danny havecompleted more of his homework than Katie?
  
• Jake has $9 and spends $1.25 each day.Finn has $14 and spends $0.75 each day.After how many days will Jake have more money than Finn?
  
• Essence has run 9 miles and she runs1.25 additional miles each day. Asia has run 14 miles and she runs 0.75 additional miles each day. After how many days will Essence have run more total miles than Asia?
  

Tags

CCSS.7.EE.B.4B

A cooler contains 4.5 gallons of water and is filling up at a rate of 0.1 gallons per second. A second cooler contains 7 gallons of water and is draining at a rate of 0.25 gallons per second. Which could be used to determine the number of seconds it would take for each cooler to contain the same amount of water?

• 4.5x + 0.1 < 7 – 0.25x
• 4.5 + 0.1x = 7 – 0.25x
• 4.5 + 0.1x = 7 + 0.25x
• 4.6x > 6.75x