Problema Solution
A car rental company has two rental rates. Rate 1 is $63 per day plus $0.18 per mile. Rate two is $126 per day plus $0.09 per mile. If you plan to rent for one week, how many miles would you need to drive to pay less by taking Rate 2?
Answer provided by our tutors
First off, 1 week = 7 days
Let C = cost
Let D = D
Let X = # of miles
Equation for Rate 1: C = 63*D + 0.18*X
Equation for Rate 2: C = 126*D + 0.09*X
We know that the car will be rented for 7 days, so we can put a 7 in for D.
We want to find out when the cost is the same so we can set the equations equal to each other.
If C = C then;
63*D + 0.18*X = 126*D + 0.09*X
Substitute the 7 in for D
63*(7) + 0.18*X = 126*(7) + 0.09*X
Simplify
441 + 0.18*X = 882 + 0.09*X
Subtract 0.09X from both sides
441 + 0.09X = 882
Subtract 441 from both sides
0.09X = 441
Divide both sides by 0.09
X = 4900
At 4900 miles, both plans cost the same amount.
Therefore you need to drive at least 4901 miles so save money with plan 2.
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