Answer:
300 miles
Step-by-step explanation:
Let
x ----> the number of miles
y ----> the total cost for rent a car
we know that
The equation of the line in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate
b is the y-intercept or initial value
Prestige car rentals
we have that
The slope is equal to [tex]m=\$0.06\ per\ mile[/tex]
The y-intercept is [tex]b=\$44[/tex]
therefore
[tex]y=0.06x+44[/tex] -----> equation A
Gateway auto
we have that
The slope is equal to [tex]m=\$0.09\ per\ mile[/tex]
The y-intercept is [tex]b=\$35[/tex]
therefore
[tex]y=0.09x+35[/tex] -----> equation B
For what number of miles both companies charge the same price>
Equate equation A and equation B
[tex]0.09x+35=0.06x+44[/tex]
solve for x
[tex]0.09x-0.06x=44-35\\0.03x=9\\x=300\ miles[/tex]
