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?

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Answer 1

Up to 2 hours or less than 2 hours Grayson charges more than Ian.

Explanation:

Grayson charges $35 per hour plus $35 administration fee.

Expression representing total charges for x hours = $(35h + 35)

Ian charges $45 per hour and an administration fee $15.

Expression representing charges for h hours = $(45h + 15)

If Grayson charges more than Ian then inequality will be

(35h + 35) ≥ (45h + 15)

Subtracting 15 form both the sides

35h + 35 - 15 ≥ 45h + 15 - 15

35h + 20 ≥ 45h

Now we subtract 35h from both the sides

35h + 20 - 35h ≥ 45h - 35h

10h ≤ 20

h ≤ 2

That means up to 2 hours or less than 2 hours Grayson charges more than Ian.

Answer 2

For any time period less than 2 hours Ian will charge less than Grayson ....

Explanation:

We have given that:

Grayson charges $35 per hour plus a $35 administration fee for tax preparation. Ian charges $45 per hour plus a $15 administration fee

The equation we get is:

45h + 15 ≤ 35h + 35

Combine the like terms:

45h-35h ≤ 35-15

10h ≤ 20

Divide both sides by 10

10h ≤ 20/10

h ≤ 2

At 2 hours the charge is the same for both services.

For any time period less than 2 hours Ian will charge less than Grayson ....