Question

The pool at "splash around" is open for 14 weeks during the summer. you can swim for $6 a session, or you can buy a membership for $100 and pay only $4 a session. which equation would you use to determine how many sessions you must use the pool to justify buying the membership?

Answer 1

Without membership:
6x14=84

with membership:
4x14=56
56+100=156

so, paying $6 a session will be cheaper for the summer, but perhaps buying the membership will be cheaper if the membership guarantees access to the pool next summer as well? not sure how to justify that. 

Answer 2

Let

x--------> the number of sessions

y-------> the total payment

we know that

without membership:

$y=6x$ --------> equation $1$

with membership:

$y=100+4x$ --------> equation $2$

using a graph tool------> resolve the system of equations

see the attached figure

the solution is the point $(50,300)$

that means

For $x=50\ sessions$

the cost is $\ 300$ in both forms

so

to justify buying the membership

$x > 50\ sessions$

therefore

the answer is

$x > 50\ sessions$