Question

Dog walker A charges $15 each day and initial set up fee of $40. Dog walker B charges $20 each day and an initial set up fee of $25. When will the two dog walkers cost the same, and what will that cost be. (Hint: y=Mx+b

Answer 1

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

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

`y=mx+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

Dog walker A

The slope or unit rate is equal to

`m=\$15\ per\ day`

The y-intercept or initial set up fee is equal to

`b=\$40`

substitute

`y=15x+40` -----> equation A

Dog walker B

The slope or unit rate is equal to

`m=\$20\ per\ day`

The y-intercept or initial set up fee is equal to

`b=\$25`

substitute

`y=20x+25` -----> equation B

Equate equation A and equation B

`20x+25=15x+40`

`20x-15x=40-25`

`5x=15`

`x=3\ days`

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

`y=15(3)+40=\$85`

equation B

`y=20(3)+25=\$85`

the cost is the same in both equations ---> is correct