Question

A grocery store bought milk for $2.70 per gallon and stored it in two refrigerators. During the night, one refrigerator malfunctioned and ruined 13 half gallons. If the remaining milk is sold for $4.04 per half gallon, how many half gallons did the store buy if they made a profit of $62.72?

Answer 1

so they bought x half gallons at $1.35 each ($2.70 per gallon). so their cost was:
C = 1.35x
Their revenue was the remainder of the milk (x - 13 that ruined) times the price:
R = 4.04(x - 13) = 4.04x - 52.52
The profit is Revenue - Cost
P = R - C = 4.04x - 52.52 - 1.35x = 2.69x - 52.52
Now we know they made 62.72 profit, so:
2.69x - 52.52 = 62.722.69x = 115.24x = 42.84 or about 43 half gallons