Answer:
Part a) The two dog walkers cost the same when the number of days is equal to 3
Part b) The cost for 3 days will be $85 for the two dog walkers
Step-by-step explanation:
Let
x ----> the number of days
y ---> the total cost 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
we have
Dog walker A
The slope or unit rate is equal to
[tex]m=\$15\ per\ day[/tex]
The y-intercept or initial set up fee is equal to
[tex]b=\$40[/tex]
substitute
[tex]y=15x+40[/tex] -----> equation A
Dog walker B
The slope or unit rate is equal to
[tex]m=\$20\ per\ day[/tex]
The y-intercept or initial set up fee is equal to
[tex]b=\$25[/tex]
substitute
[tex]y=20x+25[/tex] -----> equation B
Equate equation A and equation B
[tex]20x+25=15x+40[/tex]
[tex]20x-15x=40-25[/tex]
[tex]5x=15[/tex]
[tex]x=3\ days[/tex]
therefore
The two dog walkers cost the same when the number of days is equal to 3
Find the cost y for x=3 days
substitute in any equation (equation A or equation B)
equation A
[tex]y=15(3)+40=\$85[/tex]
equation B
[tex]y=20(3)+25=\$85[/tex]
the cost is the same in both equations ---> is correct
