SOLUTION: 5) A tennis club offers two payment options:
Option 1: $42 monthly fee plus $5/hour for court rental
Option 2: No monthly fee but $8.50/hour for court rental.
Let x = hours p
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-> SOLUTION: 5) A tennis club offers two payment options:
Option 1: $42 monthly fee plus $5/hour for court rental
Option 2: No monthly fee but $8.50/hour for court rental.
Let x = hours p
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Question 204151: 5) A tennis club offers two payment options:
Option 1: $42 monthly fee plus $5/hour for court rental
Option 2: No monthly fee but $8.50/hour for court rental.
Let x = hours per month of court rental time.
a) Write a mathematical model representing the total monthly cost, C, in terms of x for the following:
Option 1: C= 42+5x
Option 2: C= 8.50x
b) How many hours would you have to rent the court so the monthly cost of option 1 is less than option 2? Set up an inequality and show your work algebraically using the information in part a.
Answer:
Show your work here:
I try to solve for question a. where it asks me about option one C= and for Option two C=, but i have no idea if its correct. I dont know how to do the question b. Can someone help me and show me how to do this problem. My homework is due sunday at 9:59 California time. PLEASE!!!!!
You can put this solution on YOUR website! option 1 = 42 + 5*h
option 2 = 8.5*h
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you want to know when option 1 < option 2.
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your inequality equation would be:
42 + 5*h < 8.5*h
you subtract 5*h from both sides of the equation to get:
42 < 8.5*h - 5*h
you factor out the h on the right side of the equation to get:
42 < (8.5-5)*h
you simplify the right hand side of the equation to get:
42 < 3.5*h
you divide both sides of the equation by 3.5 to get:
42/3.5 < h
you simplify the left side of the equation to get:
12 < h
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12 < h is the same as h > 12
here's how you would derive it if you're not familiar with how to do it.
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start with 12 < h
subtract 12 from both sides of the equation to get:
0 < h - 12
subtract h from both sides of the equation to get:
-h < -12
multiply both sides of the equation by -1 to get:
h > 12
note that multiplying both sides of an inequality by -1 reverses the inequality.
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your answer is h > 12
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option 1 will be cheaper than option 2 when h > 12
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as a test, take h = 13
option 1 = 42 + 5*13 = 42 + 65 = 107
option 2 = 8.5*13 = 110.5
option 1 is cheaper.
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your break even point is at h = 12
that's when option 1 equation equals option 2 equation which is when:
42 + 5*h = 8.5*h
to get the break even point you have to solve the equality equation.;
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a graph of the equations looks like this.
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the line that crosses the y axis at 42 when h = 0 is your option 1 line.
the line that crosses the origin is your option 2 line.
the vertical line is when h = 12.
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when h is smaller than 12, option 1 is more expensive. when h = 12, both options are the same. when h > 12 option 1 is cheaper.
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the equations i used are:
42 + 5*h
8.5*h
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i did, however, had to change h to x in order to allow them to be graphed.
the equations for graphing purposes were:
42 + 5*x
8.5*x
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for your purposes, just change all occurrences of h to x and you will have your equations in terms of x.
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