A car rental company has two rental rates. Rate 1 is $63 per day plus $0.18 per mile. Rate 2 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?
let x = miles
126 + .09x < 63 + .18x
Solve for x.
14
To determine how many miles you would need to drive to pay less by taking Rate 2, we need to compare the total cost of each rate for one week and find the point at which Rate 2 is cheaper.
Rate 1:
Cost per day: $63
Cost per mile: $0.18
Rate 2:
Cost per day: $126
Cost per mile: $0.09
Since you plan to rent for one week, let's calculate the total cost for each rate.
Rate 1:
Total cost for one week = (cost per day x number of days) + (cost per mile x number of miles)
= ($63 x 7) + ($0.18 x number of miles)
Rate 2:
Total cost for one week = (cost per day x number of days) + (cost per mile x number of miles)
= ($126 x 7) + ($0.09 x number of miles)
To figure out the break-even point where Rate 2 becomes cheaper, we need to set the total costs equal to each other:
($63 x 7) + ($0.18 x number of miles) = ($126 x 7) + ($0.09 x number of miles)
Simplifying the equation:
441 + 0.18x = 882 + 0.09x
Subtracting 0.09x from both sides:
441 + 0.09x = 882
Subtracting 441 from both sides:
0.09x = 441
Dividing both sides by 0.09:
x = 4900
Therefore, you would need to drive 4900 miles to pay less by taking Rate 2.