Question

Write simultaneous equations to describe the situation below, solve using substitution, and fill in the blanks.

Alexa just became a personal trainer and is finalizing her pricing plans. One plan is to charge €61 for the initial consultation and then €32 per session. Another plan is to charge €66 for the consultation and €27 per session. Alexa realizes that the two plans have the same cost for a certain number of sessions. How many sessions is that? What is that cost?

For blank sessions, the cost is € blank on either plan.

Answer 1

x - the number of sessions
y - the cost

The system of equations:

`y=61+32x \\ y=66+27x`

The solution:

`y=61+32x \\ y=66+27x \\ \\ \hbox{substitute 61+32x for y in the 2nd equation:} \\ 61+32x=66+27x \\ 32x-27x=66-61 \\ 5x=5 \ \ \ |/ 5 \\ x=1 \\ \\ y=61+32x \\ y=61+32 * 1 \\ y=61+32 \\ y=93 \\ \\ (x,y)=(1,93)`

For 1 session, the cost is €93 on either plan.