Elizabeth and her sister earned money shoveling snow over winter break. altogether, they shoveled for a total of 30 hours. jenna charged her customers $12 per sidewalk, and her sister charged $11 per sidewalk. if they earned $347.50 total, how many hours did each girl spend shoveling?

Elizabeth spent 17.5 hours and her sister spent 12.5 hours.

Step-by-step explanation:

Let x be the number of hours that Elizabeth shoveled and y be the number of hours that her sister shoveled.

Number of hours they shoveled = 30

So, x + y = 30 or

y = 30 - x

Jenna charged $12 per sidewalk.

So, her total earnings = 12x

Her sister charged $11 per sidewalk.

So, her total earnings = 11y.

Their total income = $347.50.

So, 12x + 11y = 347.5

Substitute y = 30 - x,

12x + 11(30 - x) = 347.5

12x + 330 - 11x = 347.5

x + 330 = 347.5

x = 347.5 - 330

x = 17.5 and

y = 30 - x = 30 - 17.5 = 12.5.

Hence, Elizabeth spent 17.5 hours and her sister spent 12.5 hours.

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