A plumber charges $75 for the first 30 minutes of each house call plus $2 for each additional minute that she works. The plumber charges Adam $113 for her time. For what amount of time, in minutes, did the plumber work?

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Answer 1 · 2016-08-10T09:23:08

49 minutes

We can construct a formula for the plumber's fee.

$C = 75 + 2 n$ $C = color(red)(75) + color(blue)(2n)$

The red 75 denotes the $75 that is charged for the first half hour. $n$ $n$ is the number of minutes over that that she works.

Cost is $113 so

$113 = 75 + 2 n$ $113 = 75 + 2n$

Can subtract 75 from both sides of the equation without changing anything about it:

$113 - 75 = 38 = 2 n$ $113-75 = 38 = 2n$

Divide both sides by 2:

$19 = n$ $19 = n$

She worked 19 minutes over the first 30, so worked $19 + 30 = 49$ $19+30 = 49$ minutes in total.