Final answer:
To find out how many necklaces Lilly can make in 5 hours, set up a proportion based on the information given (5 necklaces in 2/5 hour) and solve for 'N'. Lilly can make 62.5 necklaces in 5 hours.
Step-by-step explanation:
The student's question involves a direct variation problem, where the number of necklaces that Lilly can make is directly proportional to the time she spends making them. We are given that Lilly can make 5 necklaces in 2/5 hour. To find out how many necklaces she can make in 5 hours, we need to set up a proportion because the number of necklaces made varies directly with the time.
Let's call the number of necklaces Lilly can make in 5 hours 'N'. Since 5 necklaces are made in 2/5 hour, we can say:
5 necklaces / (2/5 hour) = N necklaces / 5 hours
Now, to find 'N', we cross multiply:
(5 necklaces) * (5 hours) = N necklaces * (2/5 hour)
After multiplying, we get:
25 necklaces = (2/5) * N necklaces
To solve for N, we divide both sides by (2/5):
N = 25 necklaces / (2/5)
N = 25 necklaces * (5/2)
N = 62.5 necklaces
So, Lilly can make 62.5 necklaces in 5 hours.