Question

2334567Happy Paws charges $19.00 plus $2.50 per hour to keep a dog during the day. Woof Watchers charges$10.00 plus 53.75 per hour. Complete the equation and solve it to find for how many hours the total costof the services is equal. Use the variable h to represent the number of hours.The equation isThe total cost of the services will be equal athours.

Answer 1

Let h be the hours and y the total charge. Then, for Happy Paws, we have

`y=2.50h+19`

and for Woof Watches, we have

`y=3.75h+10`

Then, we need to solve these equations.

Solving by elimination method.

If we multiply by -1 the first equation, we have the equivalent system of equations:

`\begin{gathered} -y=-2.50h-19 \\ y=3.75h+10 \end{gathered}`

If we add both equations, we obtain

`0=(3.75-2.50)h+10-19`

because y-y=0. Then, it yields,

`0=1.25h-9`

If we move -9 to the left hand side as -9, we have

`\begin{gathered} 9=1.25h \\ h=(9)/(1.25) \\ h=7.2 \end{gathered}`

Hence, to find the total cost, we must substitute this values into one of the 2 equations. If we choose the first one, we obtain

`\begin{gathered} y=2.50(7.2)+19 \\ y=18+19 \\ y=37 \end{gathered}`

Then, the answers are:

The equation is

`2.50h+19=3.75h+10`

and, the total cost of the services will be equal at 7.2 hours