Question

Tonya dog- walking service charges a flat rate of $20 per month, plus $3 per mile that each dog is walked. Beth does not charge a monthly fee for her dog- walking service , but she charges $5 per mile that each dog is walked. find the miles for which Tonya and Beth will charge the same amount.

Answer 1

Given that Tonya charges 20$ monthly fee and 3$ per mile of her dog-walking service.

And Beth does not charge any monthly fee but charges 5$ per mile of the dog walked in.

Let x be the number of miles dog has walked in a month.

The amount Tonya will charge on x miles = fixed monthly fee + number of miles * charge per mile = 20+3x

And the amount Beth will charge on x miles = 0+ 5*x = 5x.

We are asked to find the x-value for which Beth chargeable amount = Tonya chargeable amount

That is 5x = 20+3x

            5x-2x = 20

              2x=20

                x=$\frac{20}{2}  = 10$

Hence number of miles for which Tonya and Beth will charge the same amount is 10.

Answer 2

Beth and Tonya would charge the same amount at 10 miles

The equation that represents the total amount charged by Tonya = flat rate + variable rate

Flat rate = $20

Variable rate = $3 x d = $3d

d = dogs walked

$20 + $3d

The equation that represents the total amount charged by Beth = $5 x d = $5d

d = dogs walked

The two equations should equal each other to determine the miles at which they would charge the same amount

$20 + $3d = $5d

Combine similar terms

$20 = $5d - $3d

$20 = $2d

Divide both sides of the equation by 2

d = 10 miles

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