A truck rental company offers two plans. One rental plan is $78 per day and $.12 per mile driven. Te other truck plan offers no daily fee but it is $.36 per mile driven. Determine the number of miles that must be driven in one day for the cost to be the same.
let the number of miles be m
.36m = .12m + 78
.24m = 78
m = 78/.24 = 325
To determine the number of miles that must be driven in one day for the cost to be the same, we can set up an equation. Let's assume the number of miles driven in one day is represented by 'm'.
For the first rental plan, the cost per day is $78 and the cost per mile is $0.12. So, the total cost for the first plan can be calculated as:
Total cost = $78 + ($0.12 * m)
For the second rental plan, there is no daily fee, so the cost is solely based on the number of miles driven. The cost per mile for this plan is $0.36. So, the total cost for the second plan can be calculated as:
Total cost = $0.36 * m
To find the number of miles that must be driven for the cost to be the same, we can equate the two total cost equations and solve for 'm'.
Setting the two total cost equations equal to each other:
$78 + ($0.12 * m) = $0.36 * m
Now, we can solve this equation for 'm':
$78 = $0.36 * m - $0.12 * m
$78 = $0.24 * m
m = $78 / $0.24
By dividing $78 by $0.24, we get:
m = 325
Therefore, in order for the cost to be the same for both plans, the number of miles that must be driven in one day is 325 miles.