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Workers load 5 identical large crates and 3 identical small crates onto a freight elevator. The crates have a combined weight of 1375 pounds. Later
that day, the workers load 3 more identical large crates and 6 more identical small crates onto the freight elevator. These crates have a combined
weight of 1350 pounds.
What is the weight of each crate?
A. Each large crate weighs 185 pounds, and each small crate weighs 150 pounds.
B. Each large crate weighs 200 pounds, and each small crate weighs 125 pounds.
C. Each large crate weighs 225 pounds, and each small crate weighs 112.5 pounds.
D. Each large crate weighs 250 pounds, and each small crate weighs 100 pounds.

Sagot :

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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.

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