# Question #72496

Jan 10, 2017

The formula for charges for the Sun Spa can be written as:

$S = 125 + 10 h$

Where $S$ is the total charges for the Sun Spa and $h$ is the number of hours used.

The formula for charges for the Moon Spa can be written as:

$M = 230 + 7 h$

Where $M$ is the total charges for the Moon Spa and $h$ is the number of hours used.

These charges would be equal when $S = M$ or when

$125 + 10 h = 230 + 7 h$

We can solve for $h$ to find the number of hours when these are equal:

$125 + 10 h - \textcolor{b l u e}{125} - \textcolor{red}{7 h} = 230 + 7 h - \textcolor{b l u e}{125} - \textcolor{red}{7 h}$

$125 - \textcolor{b l u e}{125} + 10 h - \textcolor{red}{7 h} = 230 - \textcolor{b l u e}{125} + 7 h - \textcolor{red}{7 h}$

$0 + \left(10 - 7\right) h = 105 + 0$

$3 h = 105$

$\frac{3 h}{\textcolor{red}{3}} = \frac{105}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} h}{\cancel{\textcolor{red}{3}}} = 35$

$h = 35$

For 35 hours the two spas would charge the same amount.