Final answer:
Daryl initially has 2/3 of a bag of dog food, and his dog eats 4/9 of a bag per week. By subtracting the amount eaten from the initial amount, we find that Daryl will have 2/9 of a bag of dog food remaining after one week.
Step-by-step explanation:
The student's question is about determining how much of a bag of dog food will remain after a certain period if Daryl has 2/3 of a bag and his dog eats 4/9 of a bag per week.
To solve this, we need to subtract the amount the dog eats in a week from the amount Daryl has:
Amount remaining = Amount Daryl has - Amount dog eats per week
Amount remaining = 2/3 - 4/9
To subtract these fractions, we need a common denominator, which in this case is 9. We convert 2/3 to 6/9 to make this easier:
Amount remaining = 6/9 - 4/9
When we subtract the numerators, we get:
Amount remaining = (6 - 4)/9
Amount remaining = 2/9
So, after one week, Daryl will have 2/9 of a bag of dog food left.