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

Let

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

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

we know that

without membership:

`y=6x` -------> equation A

with membership:

`y=100+4x` -------> equation B

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

the solution is the intersection both graphs

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

The equation to determine how many sessions you must use the pool to justify buying the membership is

`x> 50\ sessions`