Question 344380: Can someone help me with this word problem? A local gym charges nonmembers $10 per hour to use the tennis courts.Members pay a yearly fee of $300 and $4 per hour for using the tennis courts. Write an equation to find how many hours, h, you must use the tennis courts to justify becoming a member.Thank you!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! non-member are charged $10 an hour to use the tennis courts.
Members are charged $300 per year plus $4 per hour.
If you let x be the number of hours you use the gym in a year, then:
You will pay x * 10 if you are a non-member.
You will pay 300 + 4 * x if you are a member.
You want to know when the membership fee plus the membership cost per hour becomes less than the non-membership cost per hour.
Your formula would be:
300 + 4 * x < 10 * x
Subtract 4 * x from both sides of this equation to get:
300 < 10 * x - 4 * x
Combine like terms to get:
300 < 6 * x
Divide both sides of this equation by 6 to get:
300 / 6 < x
Simplify to get:
50 < x
This is the same as:
x > 50
The number of hours you use the tennis courts in a year has to be greater than 50 in order for becoming a member to be cheaper than remaining a non-member.
Assume the hours are 49, 50, and 51 respectively.
Non-member cost would be:
49 * 10 = 490
50 * 10 = 500
51 * 10 = 510
Member costs would be:
300 + 49*4 = 496
300 + 50*4 = 500
300 + 51*4 = 504
At 49 hours, the non-member cost is cheaper.
At 50 hours, the non-member cost and the member cdost are the same.
At 51 hours, the member cost is cheaper.
The answer provided is confirmed.
The number of hours need to be greater than 50 for the member cost to be less than the non-member cost.
|
|
|
