Answer:
The number of hours must be greater than 9 to make a Company B a better deal
Step-by-step explanation:
Let
x ----> the number of hours
y ----> the total charge in dollars
we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+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
In this problem we have
Company A
The slope is equal to [tex]m=\$10\ per\ hour[/tex]
The y-intercept is equal to [tex]b=\$80[/tex]
so
The linear equation is equal to
[tex]y=10x+80[/tex] -----> equation A
Company B
The slope is equal to [tex]m=\$5\ per\ hour[/tex]
The y-intercept is equal to [tex]b=\$125[/tex]
so
The linear equation is equal to
[tex]y=5x+125[/tex] -----> equation B
If a Company B is a better deal
then
[tex]5x+125 < 10x+80[/tex]
solve for x
[tex]125-80 < 10x-5x[/tex]
[tex]45 < 5x[/tex]
[tex]9 < x[/tex]
Rewrite
[tex]x> 9\ hours[/tex]
therefore
The number of hours must be greater than 9 to make a Company B a better deal
