Rodrigo just became a personal trainer and is finalizing his pricing plans. For one plan, Rodrigo charges $39 for the initial consultation and then $42 per session. For another plan, he charges $54 for the consultation and $39 per session. Rodrigo realizes that the two plans have the same cost for a certain number of sessions. What is that cost? How many sessions is that? Both plans cost $____ for ____ sessions.

Question

Rodrigo just became a personal trainer and is finalizing his pricing plans. For one plan, Rodrigo charges $39 for the initial consultation and then $42 per session. For another plan, he charges $54 for the consultation and $39 per session. Rodrigo realizes that the two plans have the same cost for a certain number of sessions. What is that cost? How many sessions is that?   Both plans cost $____ for ____ sessions.

Bytelearn · Accepted Answer

Set up equations:  Set up equations for the total cost of each plan after x sessions. Equate expressions:  Equate the two expressions to find the number of sessions where costs are equal. Simplify equation:  Simplify the equation by subtracting $39 and $39x from both sides. Solve for x:  Solve for x by dividing both sides by 3. Calculate total cost:  Calculate the total cost for 5 sessions using either plan.

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