Question

Jim's brakes charges $25 for parts and $55per hour to fix the brakes on the car. Myron's Auto charges $40 for parts and $30 per hour to do the same job. What length of job in hours would have the same cost at both shops?

Answer 1

See a solution process below:

Explanation:

We can write a formula for the cost of getting a job done by Jim's as:

`p_j = $25 + $55h`

We can write a formula for the cost of getting a job done by Myron's as:

`p_m = $40 + $30h`

Where `h` is the number of hours the job takes.

To find when `p_j = p_m` we can equate the right side of each equation and solve for `h`:

`$25 + $55h = $40 + $30h`

`-color(red)($25) + $25 + $55h - color(blue)($30h) = -color(red)($25) + $40 + $30h - color(blue)($30h)`

`0 + ($55 - color(blue)($30))h = $15 + 0`

`$25h = $15`

`($25h)/(color(red)($)color(red)(25)) = ($15)/(color(red)($)color(red)(25))`

`(color(red)(cancel(color(black)($25)))h)/cancel(color(red)($)color(red)(25)) = (color(red)(cancel(color(black)($)))15)/(cancel(color(red)($))color(red)(25))`

`h = 15/color(red)(25)`

`h = (5 xx 3)/color(red)(5 xx 5)`

`h = (color(red)(cancel(color(black)(5))) xx 3)/color(red)(color(black)(cancel(color(red)(5))) xx 5)`

`h = 3/5`

A job `3/5` of an hour or 36 minutes would have the same costs