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.
