Question

A car rental offers two options for renting a car. Plan A costs $200 per week plus $0.35 for each mile driven during that week. Plan B costs $180 per week plus $0.55 for each mile driven that week. How many miles of driving would result in both plans costing the same amount for that week

Answer 1

100 miles

Explanation:

Two plans are being offered for the renting of cars.

Plan A:

Cost per week = $200

Cost for each mile = $0.35

Plan B:

Cost per week = $180

Cost for each mile = $0.55

To find:

Number of miles for which the cost is same ?

Solution:

Let the number of miles driven so that the cost becomes the same =
`m` miles

First of all, let us find the cost for each plan as per
`m` miles.

Cost as per plan A = Cost per week + Cost for
`m` miles = $200 + $0.35
`m`

Cost as per plan B = Cost per week + Cost for
`m` miles = $180 + $0.55
`m`

Now, putting both the costs equal to find the value of
`m`:

`200 +0.35m = 180 +0.55m\\\Rightarrow 20 = 0.20m\\\Rightarrow m = \bold{100\ miles}`

Therefore, after 100 miles the cost from each plan will be the same.