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?

h less-than 2
h greater-than 2
h less-than 5
h greater-than 5

Answer 1

h less-than 2

Explanation:

Answer 2

h less-than 2

Explanation:

Let

h ---> the number of hours

y ---> the total charge in dollars

we know that

The linear equation is slope intercept form is equal to

`y=mh+b`

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value of the linear equation

we have

Grayson

The slope is equal to
`m=\$35\ per\ hour`

The y-intercept is
`b=\$35`

so

The total charge is equal to

`y=35h+35` ----> equation A

Ian

The slope is equal to
`m=\$45\ per\ hour`

The y-intercept is
`b=\$15`

so

The total charge is equal to

`y=45h+15` ----> equation B

For what number of hours does Grayson charge more than Ian?

The inequality that represent this situation is

`35h+35 > 45h+15`

solve for x

Group terms

`35-15 > 45h-35h`

`20 > 10h`

Divide by 10 both sides

`2 > h`

Rewrite the expression

`h< 2\ hours` ----> h less than 2 hours