Question

A grocery store bought milk for $2.80 $⁢2.80 per half gallon and stored it in two refrigerators. During the night, one refrigerator malfunctioned and ruined 13 13 half gallons. If the remaining milk is sold for $4.06 $⁢4.06 per half gallon, how many half gallons did the store buy if they made a profit of $63.14 $⁢63.14 ?

Answer 1

Let x represent the number of half-gallons purchased by the store. Then x-13 is the number sold, and 2.80x is the store's cost. The revenue is 4.06(x-13) and the difference between that and cost is the profit.

... 4.06(x -13) -2.80x = 63.14

... 1.26x - 52.78 = 63.14 . .  . . eliminate parentheses, collect terms

... 1.26x = 115.92 . . . . . . . . . . add 52.78

... x = 115.92/1.26 = 92 . . . . . divide by the coefficient of x

The store purchased 92 half-gallons of milk.