Final answer:
To board the same number of cats for a 3-day period, three-fourths of a bag of cat food will be needed if half a bag is used over a 2-day period.
Step-by-step explanation:
The question asks us to calculate the amount of cat food needed for a 3-day period, given that half a bag is used over a 2-day period. To find the answer, we can set up a proportion since the relationship between bags of food and days is linear. If half a bag is used for 2 days, then for each day, one fourth of a bag is used (half a bag divided by 2 days). Therefore, for 3 days, we would need three times one fourth, which equals three-fourths of a bag of cat food.