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Question 387990: 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.
What is the equation in question #15 for the value of h?
Kris, Thank you!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! The formula for total cost is:
T = x + y*h
x = the membership cost.
y = the cost per hour.
For the non-member, the total cost is equal to:
T = 0 + 10*h which becomes:
T = 10*h
For the member, the total cost is equal to:
T = 300 + 4*h
You want to know at what point the total cost for the member becomes less than the total cost for the non-member.
That point is given by the equation:
300 + 4*h < 10*h
Subtract 4*h from both sides of this equation to get:
300 < 10*h - 4*h
Simplify to get:
300 < 6*h
Divide both sides of this equation by 6 to get:
300/6 < h
Simplify to get:
50 < h
50 < h also means h > 50.
The total membership cost will becomes less than the total non-member cost when the number of hours is greater than 50.
If h = 50, then the equation of:
300 < 10*h - 4*h becomes:
300 < 10*50 - 4*50
Simplify this to get:
300 < 500 - 200
Simplify further to get:
300 < 300
The statement is not true because h is not greater than 50.
Take any h greater than 50 and the equation should be true.
Take h = 51.
You get:
300 < 10*51 - 4*51
simplify this to get:
300 < 510 - 204
Simplify further to get:
300 < 306
The statement is now true.
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