Final answer:
To determine how much the 34-pound dog should eat, set up a proportion based on the 15-pound dog's food intake. After setting up the proportion 15 pounds / 2 1/8 cups = 34 pounds / x cups and solving it, we find that the 34-pound dog should eat approximately 4.82 cups per day.
Step-by-step explanation:
The question deals with proportional relationships and mathematics, specifically in finding out how much dog food to feed a dog based on its weight. To solve this problem, we need to establish a ratio or proportion from the information provided and then use it to find out how much food the 34-pound dog should eat.
A 15-pound dog eats 2 1/8 cups of dog food per day. We convert 2 1/8 cups to an improper fraction which is 17/8 cups. Now, we set up the proportion:
15 pounds / (17/8 cups) = 34 pounds / x cups
By cross-multiplying we have:
15 * x = 34 * (17/8)
x = (34 * 17) / (8 * 15)
x = (578) / (120)
After simplifying the fraction, we obtain x = 4.8166 which we can round to 4.82 cups per day for a 34-pound dog.