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
[tex]y=mh+b[/tex]
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 [tex]m=\$35\ per\ hour[/tex]
The y-intercept is [tex]b=\$35[/tex]
so
The total charge is equal to
[tex]y=35h+35[/tex] ----> equation A
Ian
The slope is equal to [tex]m=\$45\ per\ hour[/tex]
The y-intercept is [tex]b=\$15[/tex]
so
The total charge is equal to
[tex]y=45h+15[/tex] ----> equation B
For what number of hours does Grayson charge more than Ian?
The inequality that represent this situation is
[tex]35h+35 > 45h+15[/tex]
solve for x
Group terms
[tex]35-15 > 45h-35h[/tex]
[tex]20 > 10h[/tex]
Divide by 10 both sides
[tex]2 > h[/tex]
Rewrite the expression
[tex]h< 2\ hours[/tex] ----> h less than 2 hours