Tennis Club 2 Options #1 $32/month +$3hour Fee Or $0 Month +$6.50 Fee, X=hours Per Month Fee.
Write a mathmatical model for the total monthly cost, \"C\" in terms of x for the following: Option 1: C= Option 2: C= How many hours would you have to rent the court so that the monthly cost of option 1, is less than option 2?
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C1 = $32 + ($3/hr)*(x hr) = $(32+3x)
C2 = ($6.50/hr)*(x hr) = $(6.5x)
We want C12
$(32+3x) < $(6.5x) (substitute the expressions for cost)
32 < 3.5x (divide by $, subtract 3x from both sides)
32/3.5 < x (divide both sides by 3.5)
9.14 < x (evaluate and approximate by 2 decimal digits)
You would have to rent the court more than 9 hours 9 minutes per month to make the monthly cost of Option 1 be less than that of Option 2.
C2 = ($6.50/hr)*(x hr) = $(6.5x)
We want C1
$(32+3x) < $(6.5x) (substitute the expressions for cost)
32 < 3.5x (divide by $, subtract 3x from both sides)
32/3.5 < x (divide both sides by 3.5)
9.14 < x (evaluate and approximate by 2 decimal digits)
You would have to rent the court more than 9 hours 9 minutes per month to make the monthly cost of Option 1 be less than that of Option 2.
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