A rental car agency charges $240 per week plus $0.25 per mile to rent a car. The charge for a minivan is $180 per week plus $0.40 per mile. After how many miles is the total charge for each vehicle the same?

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rejkjavik rejkjavik · Answer 1 · 2018-11-01T03:24:58+01:00

Rental car agency charge:

Let's assume number of miles in as week as x miles

and total rent as R(x)

A rental car agency charges $240 per week plus $0.25 per mile to rent a car

so, we get equation as

[tex]R(x)=240+0.25x[/tex]

Minivan charge:

Let's assume number of miles in as week as 'x' hours

and total charge of minivan as M(x)

The charge for a minivan is $180 per week plus $0.40 per mile

so, we get

[tex]M(x)=180+0.40x[/tex]

now, we can set them equal

and then we can solve for x

[tex]240+0.25x=180+0.40x[/tex]

Subtract both sides by 0.25x

[tex]240+0.25x-0.25x=180+0.40x-0.25x[/tex]

[tex]240=180+0.15x[/tex]

Subtract both sides by 180

[tex]240-180=180+0.15x-180[/tex]

[tex]60=0.15x[/tex]

divide both sides by 0.15

and we get

[tex]x=400 miles/tex]............Answer