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 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 total cost will never be the same.

The graph below 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 have earned 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.

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

Identify the equation modeled, and then find its solution.

• Equation: 4x + 4 = -x + 1

  Solution: x = -0.6

• Equation: -4x + 4 = -x - 1

  Solution: x = 1.66666666666

• Equation: 4x - 4 = -x - 1

  Solution: x = 0.6

• Equation: 4x - 4 = -x - 1

  Solution: x = 1

• 6 weeks

• 12 weeks

• 2 weeks

• 7 weeks

• Less than 10 minutes

• Less than 7 minutes

• More than 10 minutes

• More than 13 minutes

Which of the following can be determined from the graph?

• The ordered pair (6, 25) is a solution to both y = 5/2x + 40 and y = 5/3x + 15.

• The ordered pair (25, 6) is a solution to both y = 5/2x + 40 and y = 5/3x + 15.

• The ordered pair (6, 25) is a solution to both y = 5/2x + 40 and y = -5/3x + 15.

• The ordered pair (6, 25) is a solution to both y = -1/2x + 40 and y = 1/3x + 15.

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

9 + 1.25x > 14 + 0.75x

• Park A charges an entrance fee of $9 plus $1.25 per ride. Park B charges $14 per ride 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 problems every 9 minutes. Katie finishes 0.75 homework problems every 14 minutes. After how many minut4s will Danny have completed 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 runs 1.25 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?

• 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

What value of x that would make the equation modeled true.

• 1.25

• -1.25

• .25

• -.25