a car rental company has two rental rates. Rate 1 is $56 per day plus $.16 per mile. Rate 2 is $112 per day plus $.08 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?
56 + .16x > 112 + .08x
Solve for x.
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 renting under both rates for one week.
Rate 1: $56 per day plus $0.16 per mile
Rate 2: $112 per day plus $0.08 per mile
Let's calculate the total cost under Rate 1 for one week. Since there are 7 days in a week, the total cost under Rate 1 would be:
Total Cost under Rate 1 = Rate per day * Number of days + Cost per mile * Number of miles
= $56 * 7 + $0.16 * Number of miles
= $392 + $0.16 * Number of miles
Now, let's calculate the total cost under Rate 2 for one week:
Total Cost under Rate 2 = Rate per day * Number of days + Cost per mile * Number of miles
= $112 * 7 + $0.08 * Number of miles
= $784 + $0.08 * Number of miles
To find the number of miles you would need to drive for Rate 2 to be less expensive than Rate 1, we need to equate the two total costs and solve for the number of miles:
$392 + $0.16 * Number of miles = $784 + $0.08 * Number of miles
Subtract $0.08 * Number of miles from both sides:
$392 + $0.08 * Number of miles - $0.08 * Number of miles = $784
Combine like terms:
$392 = $784
Since the equation is not true, it means that there is no number of miles you can drive for Rate 2 to be less expensive than Rate 1 when renting for one week.