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.

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=

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

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form