Final answer:
To check the correctness of the student's mixture of 8 scoops with 2 gallons of water for 4 pitchers of juice, we establish the ratio for one pitcher and scale it to match the desired quantity. If the ratio calculated matches the student's mixture, then they are correct.
Step-by-step explanation:
To determine if the student is correct in mixing 8 scoops with 2 gallons of water to make 4 pitchers of juice, we can use the concept of proportional relationships or ratios. We'll tackle this question by first establishing what the recipe for a single pitcher is, then scaling it up to 4 pitchers.
Let's assume that the known ratio for one pitcher of juice is 'x scoops' per gallon. To find out how many scoops are needed for 2 gallons, you would double the amount of 'x scoops' (since 2 gallons would require twice the number of scoops as 1 gallon). If this results in the 8 scoops the student intends to use for 2 gallons, then the original ratio 'x scoops' per gallon was indeed 4 scoops per gallon, which is correct for 4 pitchers (assuming each pitcher requires a half-gallon of this juice mixture).