Answer:
B. Each large crate weighs 200 pounds, and each small crate weighs 125 pounds.
Step-by-step explanation:
Let L be the weight of the large crate and S the weight of the small crate.
Given that 5 identical large crates and 3 identical small crates have a combined weight of 1375 pounds,
5L + 3S = 1375 (1)
Also, in the second loading 3 identical large crates and 6 identical small crates have a combined weight of 1350 pounds,
3L + 6S = 1350 (2)
multiplying equation (1) by 2 and (2) by 1, we have
5L + 3S = 1375 (1) × 2
3L + 6S = 1350 (2) × 1
10L + 6S = 2750 (3)
3L + 6S = 1350 (4)
Subtracting (4) from (3), we have
7L = 1400
dividing through by 7, we have
L = 1400/7
L = 200
Substituting L = 200 into (1), we have
5L + 3S = 1375 (1)
5(200) + 3S = 1375 (1)
1000 + 3S = 1375
3S = 1375 - 1000
3S = 375
dividing through by 3, we have
S = 375/3
S = 125
So, each large crate weighs 200 pounds, and each small crate weighs 125 pounds.