You wash dishes for a chemistry laboratory to make extra money for laundry. You earn 12 dollars/hour, and each shift lasts 75 minutes. Your laundry requires 12 quarters/load. Part AHow many shifts must you work if you wish to wash 10 loads of laundry

2 shifts

Step-by-step explanation:

Amount earned washes dishes = 12 dollars / hour

Shift duration = 75 minutes

Cost of laundry = 12 quarters per load

Cost of 10 loads of laundry = (10 * 12 quarters) = 120 quarters

1 quarter = 25 cents

120 quarters = (25 * 120) = 3000 cents

100 cents = $1

3000 cents = 3000/ 100 = $30

Hence, to make $30 from washing dishes :

$12 = 1 hour

$30 = x

x = 30 / 12

x = 2.5 hours

1 shift lasts 75 minutes

2.5 hours = (2.5 * 60) = 150 minutes

150 / 75 = 2 shifts

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4