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?

1 Answer
Nile River
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= 1.5x+ 19#

Woof Watchers
#y= 2.75x+ 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' #2.75x +15# into the #y# of Happy Paws.

#2.75x+ 15= 1.5x+ 19#

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

#1.25x= 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(3.2)+ 19= 23.8#
Woof Watchers: #2.75(3.2) + 15= 23.8#

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