A rock-climbing gym charges non-members $16.00 per day to sue the gym and $8.00 per day for equipment rental. Members pay a yearly fee of $450.00 fro unlimited climbing and $6.00 per day for equipment rental. Write and solve equation to find how many times you must use the gym to justify becoming a member.
I hope we are to use the gym before suing it.
n days
member cost = 450 + 6 n
vistor cost = 24 n
so
24 n = 450 + 6 n
18 n = 450
n = 25 days
To find out how many times you must use the gym to justify becoming a member, we need to calculate the cost of using the gym as a non-member and compare it to the cost of being a member.
Let's represent the number of times you use the gym as "x".
As a non-member, the cost of using the gym would be $16.00 per day plus $8.00 per day for equipment rental. So, the cost of using the gym as a non-member is: 16x + 8x = 24x.
As a member, the cost of using the gym is covered by the yearly fee of $450.00 for unlimited climbing. However, you still need to pay $6.00 per day for equipment rental. Therefore, the cost of using the gym as a member is: 6x.
To justify becoming a member, the cost of using the gym as a non-member should be equal to or greater than the cost of being a member. In equation form, this can be expressed as:
24x ≥ 450 + 6x
Now, let's solve the equation to find the value of x:
24x - 6x ≥ 450
18x ≥ 450
x ≥ 450 / 18
x ≥ 25
So, you must use the gym at least 25 times to justify becoming a member.