Final answer:
The food supply will last for 37 days.
Step-by-step explanation:
To determine how many days the food supply will last, we need to divide the total amount of grain by the amount of grain each cow eats per day. First, we calculate the total amount of grain eaten by all the cows in one day by multiplying the amount of grain eaten by one cow by the number of cows: 12 pounds/cow * 24 cows = 288 pounds/day. Then, we divide the total amount of grain by the amount eaten per day: 10,656 pounds / 288 pounds/day = 37 days. Therefore, the food supply will last for 37 days.