Question

Happy kids charge $19.00 plus $1.50 per hour to keep a kid during the day. Fun city charges $14.00 plus $2.75 per hour. Write and solve an equation to find for how many hours the total cost of the services is equal. (70 points!)

Answer 1

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
(
3.2
)
+
19
=
23.8

Woof Watchers:
2.75
(
3.2
)
+
15
=
23.8

Answer 2

Answer: y = 1.50x + 19 and y = 2.75x + 14
y = 25
x = 4
Both services will charge an equal cost of $25 for 4 hours.