Question

Ben wants to join a fitness club. The fitness club charges an initial membership fee of $49.50 and a monthly fee of $17.50.

Question 1
Part A

Ben has $172 to spend on a membership at the fitness club. How many months can Ben be a member of the fitness club?

Ben has enough money to be a member of the fitness club for months.
Question 2
Part B

Ben’s company will pay $300.00 each year toward his fitness club membership. Ben thinks he will have to pay $40.50 for his membership his first year. Is he correct?

Use the drop-down menus to explain your reasoning.

The total cost for a membership at the fitness club for the first year is $________. Ben's company will pay $300.00 each year, so Ben will have to pay $________ for his membership the first year. Ben’s thinking is_______ .

Answer 1

Question 1
 The first thing we must do for this case is to write the linear function that adapts to the problem.
 We have then:
 f (x) = 17.50x + 49.50
 Where,
 f (x): total payment
 x: number of months.
 For f (x) = 172 we have:
 172 = 17.50x + 49.50
 We clear x:
 x = (172-49.50) / (17.50)
 x = 7
 Answer:
 Ben has enough money to be a member of the fitness club for 7 months
 Question 2
 For this case we must use the equation found in the previous question.We have then:
 f (x) = 17.50x + 49.50
 One year has 12 months. We then evaluate the equation for x = 12:
 f (12) = 259.5
 We observed that;
 259.5 <300
 Therefore, Ben should not pay anything.
 Answer:
 The total cost for a membership at the fitness club for the first year is $ 259.5. Ben's company will pay $ 300.00 each year, so Ben will have to pay $ 0 for his membership the first year. Ben's thinking is not correct.