The formula for charges for the Sun Spa can be written as:
S = 125 + 10h
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 + 7h
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 + 10h = 230 + 7h
We can solve for h to find the number of hours when these are equal:
125 + 10h - color(blue)(125) - color(red)(7h) = 230 + 7h - color(blue)(125) - color(red)(7h)
125 - color(blue)(125) + 10h - color(red)(7h) = 230 - color(blue)(125) + 7h - color(red)(7h)
0 + (10 - 7)h = 105 + 0
3h = 105
(3h)/color(red)(3) = 105/color(red)(3)
(color(red)(cancel(color(black)(3)))h)/cancel(color(red)(3)) = 35
h = 35
For 35 hours the two spas would charge the same amount.
