Question

Kendall just became a personal trainer and is finalizing her pricing plans. One plan is to charge $37 for the initial consultation and then $33 per session. Another plan is to charge $101 for the consultation and $32 per session. Kendall realizes that the two plans have the same cost for a certain number of sessions. How many sessions is that? What is that cost?

Answer 1

After 64 sessions, the cost of both of Kendall's plans would be the same, which would be $2149.

Step-by-step explanation:

Kendall's two pricing plans can be represented by linear equations. Plan 1 is $37 + $33 per session, while Plan 2 is $101 + $32 per session. To find out after how many sessions the cost would be the same, we set the two equations equal to each other:

37 + 33x = 101 + 32x

This simplifies to:

33x - 32x = 101 - 37

x = 64

So, after 64 sessions, the cost of both plans would be equal. To find that cost, we substitute x back into either equation:

Total cost for Plan 1 = 37 + 33(64) = $2149

Therefore, the cost for 64 sessions is $2149 using either plan.

Answer 2

The 2 Plan will have same cost of $2149 after 64 sessions.

Step-by-step explanation:

Given;

Let the Two plan be Plan A and Plan B.

Also let the number of session be
`x`

According to given detail

Plan A =
`\$37+33x`

Plan B =
`\$101+32x`

We need to find the value of when both are equal.

Plan A = Plan B

`\$37+33x` =
`\$101+32x`

Solving above equation we get;

`33x-32x=101-37\\x=64`

Number of session are 64.

Cost after 64 session will be,

Plan A =
`\$37+\$33x=\$37+\$33* 64 = \$37+\$2112 = \$2149`

Plan B =
`\$101+\$32x=\$101+\$32* 64 = \$101+\$2048 = \$2149`

Hence The 2 Plan will have same cost of $2149 after 64 sessions.