Question

A grocery store bought milk for $2.40 per half gallon and stored it in two refrigerators. During the night, one refrigerator malfunctioned and ruined 14 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 $107.44?

Answer 1

Explanation:

Let's start by figuring out how many half gallons of milk the store had before the refrigerator malfunctioned.

The store bought the milk for $2.40 per half gallon, so the cost of the milk before the malfunction was:

cost_before = 2.40 * x

where x is the number of half gallons of milk the store bought.

After the malfunction, the store had x - 14 half gallons of milk left. The store sold the remaining milk for $4.04 per half gallon, so the revenue from selling the remaining milk was:

revenue_after = 4.04 * (x - 14)

The store's profit is equal to the revenue minus the cost, so we can write:

profit = revenue_after - cost_before

Substituting in the expressions we found earlier, we get:

107.44 = 4.04 * (x - 14) - 2.40 * x

Simplifying this equation, we get:

107.44 = 1.64x - 56.56

Adding 56.56 to both sides, we get:

164.00 = 1.64x

Dividing both sides by 1.64, we get:

x = 100

So the store bought 100 half gallons of milk before the refrigerator malfunctioned.