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?

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

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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?
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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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