Final answer:
Luca will need to purchase 51 bags of dog food to feed his dog Josie for one year, calculated by multiplying Josie's daily consumption by 365 days and then dividing by the number of cups per bag.
Step-by-step explanation:
Luca's dog Josie eats 2.5 cups of dog food a day. To find out how many bags of dog food Luca would need for one year, first, we calculate the total amount of dog food Josie will eat in a year by multiplying the daily amount by 365 days:
2.5 cups/day × 365 days = 912.5 cups per year
Next, we divide this annual consumption by the amount of dog food in one bag:
912.5 cups ÷ 18 cups/bag = 50.6944 bags
Since Luca cannot purchase a fraction of a bag, he will need to buy 51 bags of dog food to ensure that Josie has enough to eat for an entire year. It is important to always round up in cases where you're dealing with a necessity that cannot be acquired in fractions, such as bags of dog food.