Final answer:
Mervin initially had 480 cartons of milk. He sold 2/5 in the morning and 3/4 of the remainder in the afternoon, with a difference of 24 more cartons sold in the afternoon compared to the morning.
Step-by-step explanation:
The question asks us to find the number of cartons of milk Mervin had initially. Mervin sold 2/5 of his cartons of milk in the morning and then 3/4 of the remainder in the afternoon, with 24 more cartons being sold in the afternoon than in the morning.
Let's assume Mervin started with x cartons of milk. In the morning, he sold 2/5 of them, so he had 3/5 of x cartons left. In the afternoon, he sold 3/4 of the remaining cartons. This means he had 1/4 of 3/5 of x cartons left, equating to 3/20 of x. Since he sold 24 more cartons in the afternoon than in the morning, we can set up the equation: (3/4) * (3/5 * x) - (2/5 * x) = 24.
To solve for x, simplify the equation: 9/20x - 8/20x = 24 which simplifies to 1/20x = 24. Multiplying both sides by 20 gives us x = 480. This means Mervin had 480 cartons of milk at first.