Question

A grocery store bought ice cream for $2.50 per gallon and stored it in two freezers. During the night, one freezer malfunctioned and ruined 13 half gallons. If the reamining ice cream is sold for $3.98 per half gallon, how many half gallons did the store buy if they made a profit of $84.42?

Answer 1

Let x be the number of half gallons they bought. (2.50/2)x is how much they paid for those half gallons (notice that the price is given per gallon, not half gallon.) They lost 13 half gallons when the freezer messed up, so now they have (x - 13) half gallons left. They sold those for 3.98 a pop, so the amount of money they made is 3.98(x - 13). Now we have enough info:
\[Profit = Revenue - Cost \Rightarrow 84.42 = 3.98(x - 13) - \frac{2.50}{2} x\]
\[\Rightarrow 84.42 = 3.98x-3.98(13)-1.25x\Rightarrow x = \frac{84.42+3.98(13)}{3.98-1.25}\]
Which gives us an answer of 49.87, so I guess 50 half gallons.