Question

Grayson charges $35 per hour plus a $35 administration fee for tax preparation. Ian charges $45 per hour plus a $15 administration fee. If h represents the number of hours of tax preparation, for what number of hours does Grayson charge more than Ian?

Answer 1

Answer: After 2 hours period, Grayson charges more than Ian.

Explanation:

Let h represents the number of hours of tax preparation.

Given : Grayson charges $35 per hour plus a $35 administration fee for tax preparation.

Ian charges $45 per hour plus a $15 administration fee.

Also, Total charges = Admiration fee + rate per hour × (number of hours of tax preparation)

⇒ Expression for charges done by Grayson:-

`G(h)=35+35h`

Expression for charges done by Ian:-

`I(h)=15+45h`

Required equation :-

`G(h)>I(h)\\\\ 35+35h>15+45h`

Subtract 15 and 35 h from both sides , we get

`20>10h`

Divide both sides by 10, we get

`2>h`

⇒ Any hours greater than 2 , Grayson charges more than Ian.

⇒ After 2 hours period, Grayson charges more than Ian.

Answer 2

We translate Grayson's charges through the following mathematical expression : 35 h + 35 where h is the number of hours while that of Ian is 45h + 15. The number of hours where the charges are equal is 35h + 35 = 45h + 15; h = 2 hrs. Hence the number of hours minimum must be above 2 hours.