Let h be the hours and y the total charge. Then, for Happy Paws, we have
[tex]y=2.50h+19[/tex]
and for Woof Watches, we have
[tex]y=3.75h+10[/tex]
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:
[tex]\begin{gathered} -y=-2.50h-19 \\ y=3.75h+10 \end{gathered}[/tex]
If we add both equations, we obtain
[tex]0=(3.75-2.50)h+10-19[/tex]
because y-y=0. Then, it yields,
[tex]0=1.25h-9[/tex]
If we move -9 to the left hand side as -9, we have
[tex]\begin{gathered} 9=1.25h \\ h=\frac{9}{1.25} \\ h=7.2 \end{gathered}[/tex]
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
[tex]\begin{gathered} y=2.50(7.2)+19 \\ y=18+19 \\ y=37 \end{gathered}[/tex]
Then, the answers are:
The equation is
[tex]2.50h+19=3.75h+10[/tex]
and, the total cost of the services will be equal at 7.2 hours
