Question #72496

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Answer 1 · 2017-01-10T22:31:56

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

$S = 125 + 10 h$ $S = 125 + 10h$

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

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

$M = 230 + 7 h$ $M = 230 + 7h$

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

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

$125 + 10 h = 230 + 7 h$ $125 + 10h = 230 + 7h$

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

$125 + 10 h - 125 - 7 h = 230 + 7 h - 125 - 7 h$ $125 + 10h - color(blue)(125) - color(red)(7h) = 230 + 7h - color(blue)(125) - color(red)(7h)$

$125 - 125 + 10 h - 7 h = 230 - 125 + 7 h - 7 h$ $125 - color(blue)(125) + 10h - color(red)(7h) = 230 - color(blue)(125) + 7h - color(red)(7h)$

$0 + (10 - 7) h = 105 + 0$ $0 + (10 - 7)h = 105 + 0$

$3 h = 105$ $3h = 105$

$\frac{3 h}{3} = \frac{105}{3}$ $(3h)/color(red)(3) = 105/color(red)(3)$

$(color(red)(cancel(color(black)(3)))h)/cancel(color(red)(3)) = 35$

$h = 35$

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