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.