Question

Brendan just became a personal trainer and is finalizing his pricing plans. One plan is to charge $50 for the initial consultation and then $60 per session. Another plan is to charge $100 for the consultation and $50 per session. Brendan realizes that the two plans have the same cost for a certain number of sessions. After how many sessions will the pricing be the same?

Answer 1

To find the session count where both pricing plans are equal, equations are set up for each plan and solved algebraically to find that after 5 sessions, the pricing would be the same.

Step-by-step explanation:

The student's question pertains to finding the number of sessions after which two different pricing plans offered by a personal trainer will cost the same amount. To solve this, we can set up two equations representing the total cost for each plan and then solve for the number of sessions where both costs are equal.

For the first plan: the cost is $50 for the consultation plus $60 per session. So, if x represents the number of sessions, the total cost T1 is T1 = 50 + 60x.

For the second plan: the cost is $100 for the consultation plus $50 per session. So, the total cost T2 is T2 = 100 + 50x.

To determine after how many sessions the pricing will be the same, set T1 equal to T2: 50 + 60x = 100 + 50x. Solving for x involves subtracting 50x from both sides to get 10x = 50, and then dividing both sides by 10 to find x = 5.

Therefore, after 5 sessions, the cost of both pricing plans will be the same.