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?

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?

anonymous · Answer

This is the exact same problem as the last one (half gallons of ice cream), so lets just switch numbers out.
$$x = \frac{62.72+4.04(13)}{4.04-\frac{2.70}{2}}$$
x = 42.8 or 43 half gallons.

anonymous · Answer

http://openstudy.com/groups/mathematics#/groups/mathematics/updates/4e0f7c0a0b8b56e555981fbb

anonymous · Answer

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 = 62.72
2.69x = 115.24
x = 42.84 or about 43 half gallons