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 represent the number of hours of tax preparation, for what number of hours does Grayson charge more than Ian?

Answer 1

Here, h represents the number of hours for which Grayson charges more than Ian,

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

Thus, the charges of Grayson after h hours = ( 35h + 35 ) dollars,

Also, Ian charges $45 per hour plus a $15 administration fee,

Thus, the charges of Ian after x hours = ( 45x + 15 ) dollars,

⇒ 35h + 35 > 45x + 15

⇒ 35 - 15 > 45x - 35x

⇒ 20 > 10x

⇒ 2 > x

Hence, for the hours less than 2 ( and more than equal to 0 ) Grayson charge more than Ian.