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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?

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meerkat18
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. 
JeanaShupp

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

Step-by-step 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:-

[tex]G(h)=35+35h[/tex]

Expression for charges done by Ian:-

[tex]I(h)=15+45h[/tex]

Required equation :-

[tex]G(h)>I(h)\\\\ 35+35h>15+45h[/tex]

Subtract 15 and 35 h from both sides , we get

[tex]20>10h[/tex]

Divide both sides by 10, we get

[tex]2>h[/tex]

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

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

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