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

Answer:

h less-than 2

Step-by-step explanation:

Answer 2

Answer:

h less-than 2

Step-by-step 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