Final answer:
The contractor purchased 5 small boxes and 10 large boxes.
Step-by-step explanation:
To determine the number of small and large boxes purchased, we can set up a system of equations based on the given information. Let's let 's' represent the number of small boxes and 'l' represent the number of large boxes.
From the given information, we know that each small box has 200 nails and each large box has 500 nails. This means that the total number of nails in the small boxes is 200s and the total number of nails in the large boxes is 500l.
According to the given information, the contractor bought twice as many large boxes as small boxes, which altogether had 6000 nails. So we can set up the following equations:
200s + 500l = 6000
l = 2s
We can substitute the value of l from the second equation into the first equation:
200s + 500(2s) = 6000
200s + 1000s = 6000
1200s = 6000
s = 5
Substituting the value of s back into the second equation, we can find the value of l:
l = 2(5)
l = 10
Therefore, the contractor purchased 5 small boxes and 10 large boxes.