Question

You rent a car for the day and are offered two payment options. With option A you pay $25 flat rate plus $0.15 per mile. With option B you pay a $10 flat rate plus $0.40 per mile. For what amount of miles would the cost of option A be equal to option B

Answer 1

60 miles.

Explanation:

Given:

We rent a car for the day and are offered two payment options.

With option A we pay $25 flat rate plus $0.15 per mile.

With option B we pay a $10 flat rate plus $0.40 per mile.

Question asked:

For what amount of miles would the cost of option A be equal to option B ?

Solution:

Let amount of miles for which the cost of option A be equal to option B =
`x`

For option A, we pay =
`25+0.15* x`

For option B, we pay =
`10+0.40* x`

Now, to find amount of miles for which the cost of option A be equal to option B, we will equalize the equation to find the value of
`x`

`25+0.15x=10+0.40x\\`

By subtracting both sides by 10

`25-10+0.15x=10-10+0.40x\\15+0.15x=0.40x`

By subtracting both sides by
`0.15x`

`15+0.15x-0.15x=0.40x-0.15x\\15=0.25x`

By dividing both sides by
`0.25`

`x=60\ miles`

Therefore, for 60 miles, the cost of option A will be equal to option B.