Final answer:
To make the total costs at Fit4like and Gym Time equal, one can set the equation for each gym's total cost equal to each other and solve for the number of personal training sessions. Upon solving the equation, Jacob would need to buy 2 personal training sessions, which is not listed among the answer choices provided.
Step-by-step explanation:
To find out how many personal training sessions Jacob would have to buy to make the total cost at Fit4like and Gym Time equal, we need to create an equation that represents the cost for each gym and then solve for the number of personal training sessions.
Let's denote the number of personal training sessions Jacob buys with the variable x. For Fit4like, the total cost (C1) is the cost of membership ($15) plus the cost of personal training sessions ($40 each), which we can express as:
C1 = 15 + 40x
For Gym Time, the total cost (C2) is the cost of membership ($55) plus the cost of personal training sessions ($20 each), expressed as:
C2 = 55 + 20x
To make the total costs equal, we set C1=C2:
15 + 40x = 55 + 20x
Subtracting 20x from both sides of the equation, we get:
15 + 20x = 55
Subtracting 15 from both sides, we have:
20x = 40
Dividing both sides by 20 gives us:
x = 2
Therefore, Jacob would have to buy 2 personal training sessions to make the total costs at the two gyms equal. However, this solution is not listed in the given options. It seems there might be an error in the question or answer choices provided.