Happy Paws charges $19.00 plus$1.50 per hour to keep a dog during the day. Woof Watchers charges $15.00 plus$2.75 per hour. How do you write and solve and equation to find for how many hours the total cost of services is equal?

Feb 13, 2016

After 3.2 or 3 hours and 12 minutes, the total cost of services is equal.

Explanation:

First, set up equations for total cost for both Happy Paws and Woof Watchers.

x= number of hours
y= total cost

Happy Paws
$y = 1.5 x + 19$

Woof Watchers
$y = 2.75 x + 15$

Because you have to find when total cost is equal, then the y's of both equations are equal to each other. That means you can substitute the Woof Watchers' $2.75 x + 15$ into the $y$ of Happy Paws.

$2.75 x + 15 = 1.5 x + 19$

Rearrange the equation so the variable, x, is on one side and the numbers on the other and solve.

$1.25 x = 4$
$x = 3.2$

You can check the answer by plugging $3.2$ into x in the two equations and see if they yield the same total cost

Happy Paws: $1.5 \left(3.2\right) + 19 = 23.8$
Woof Watchers: $2.75 \left(3.2\right) + 15 = 23.8$