Question

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Mai earns $7 per hour mowing her neighbors' lawns. She also earned $14 for hauling away bags of recyclables for some neighbors.

Priya babysits her neighbor’s children. The table shows the amount of money m she earns in h hours. Priya and Mai have agreed that when their earnings are the same, they will go to the movies together.

h m
1 $8.40
2 $16.80
4 $33.60
How many hours do they have to work before they go to the movies?

_____hours

How much will they have earned?
$_____

Answer 1

Answer: they worked 11 hours in total. (Mai works 6 hours and Priya works 5 hours) they will have earned $98. Without adding the extra $14 it’s $84.

Answer 2

Let m and h represent hours Mai spends mowing and hauling, respectively. Then (m+h) will be the number of hours Priya spends babysitting. In order for their earnings to be equal, we must have

7m +14h = 8.40(m+h)

Subtract 7m+8.40h: 5.60h = 1.40m

Divide by 1.40: m = 4h

Then the total number of hours worked by either person is

m + h = (4h) +h = 5h

When only whole numbers of hours are worked, the smallest number of hours that will make earnings equal is 5h, with h=1, or 5 hours. In that time, each will earn 5×$8.40 = $42.

Therefore, each of them must work 5 hours and earn $42 before they go to the movies and Mai will work 4 hours mowing and 1 hour hauling.