A local computer center charges non-members $5.00 per session to use the media center. If you pay a membership fee of $25, you pay only $3 per session. Write an equation that can help you decide whether to become a member then solve the equation and interpret the solution.
You save $2 per session. How many sessions do you have to have to equal or exceed your membership fee?
I hope this helps. Thanks for asking.
C1 = 5x (non-members)
C2 = 3x + 25 (members)
So by equating these two functions, we can find out for how many sessions (x) it would be better to become a member.
5x = 3x + 25
2x = 25
x = 12.5 (12 or 13, we can't have half a session)
check: for 13 sessions
C1 = 65
C2 = 64
So for 13 or more sessions it would be cheaper to become a member, for sessions less than 13 the "pay-as-you-go" plan would be cheaper.
BTW Amber, it is not a good idea to use your full name on a public webpage like this. Your first name or some nickname is sufficient.
Let's start by defining some variables:
Let:
x = the number of sessions used
C = cost of using the media center for non-members
M = cost of using the media center for members
According to the given information:
C = $5.00 per session
M = $3.00 per session
For non-members, the equation is:
Cost for non-members = C * x = 5.00 * x
For members, the equation is:
Cost for members = M * x = 3.00 * x
If you choose to become a member, you need to pay a membership fee of $25 upfront.
The equation to help you decide whether to become a member is:
Cost for non-members = Cost for members
Substituting the values we have:
5.00 * x = 3.00 * x + 25
To solve this equation, we can start by subtracting 3.00 * x from both sides:
5.00 * x - 3.00 * x = 3.00 * x + 25 - 3.00 * x
2.00 * x = 25
Then, divide both sides by 2.00 to isolate x:
x = 25 / 2.00
x = 12.5
Interpreting the solution:
The solution, x = 12.5, tells us that if you plan to use the media center for 12.5 sessions or more, it is more cost-effective to become a member. If you use fewer than 12.5 sessions, it is cheaper to pay the non-member rate of $5.00 per session. Since you can't have a fractional number of sessions, you can round up the result to the nearest whole number, in this case, 13. Thus, you should become a member if you plan to use the media center for 13 or more sessions.
To determine whether becoming a member is more cost-effective, we can set up an equation.
Let's assume x represents the number of sessions a person plans to use the media center.
For non-members:
cost per session = $5.00
total cost for x sessions = 5x
For members:
cost per session = $3.00
membership fee = $25.00
total cost for x sessions = 3x + 25
To decide whether to become a member, we need to compare the total cost for x sessions as a non-member ($5x) with the total cost for x sessions as a member (3x + 25). Setting up the equation:
5x > 3x + 25
Now, let's solve the equation:
5x - 3x > 25
2x > 25
x > 12.5
The solution is x > 12.5, which means that if you plan to use the media center for more than 12 sessions, it would be more cost-effective to become a member.
Interpretation:
If you plan to use the media center for 12 or fewer sessions, it is better to pay $5 per session as a non-member. However, if you plan to use the media center for more than 12 sessions, it is more cost-effective to pay the $25 membership fee and enjoy the reduced rate of $3 per session.