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

$x> 50\ sessions$

Answer 2

Price before membership= price 1 = $6
price after membership = price 2 = $4
Membership price = $100
SO according to price 1 and price 2; price after membership saves up $2 for each session.
Hence to justify the price of membership number of sessions can be calculated as follows:-
$2 saved = 1 session
to make it $100 multiply both sides by 50
2×50 = 1×50
100$ saved = 50 sessions
so 50 sessions ate required to justify buying the membership.


Hope this helped :)