Answer:
The weight of a small box = 13.5 kg
The weight of 1 large box = 18.5 kg
Step-by-step explanation:
Let us assume the weight of a small box = m kg
And the weight of 1 large box = n kg
Now, the weight of 5 small box = 5 x (weight of 1 small box) = 5 m
Also, the weight of 3 large box = 3 x (weight of 1 large box) = 3 n
Here, 3 large boxes + 5 small boxes = of 123 kilograms
⇒ 5 m + 3 n = 123 .... (1)
Again, the weight of 2 small box = 2 x (weight of 1 small box) = 2 m
Also, the weight of 12 large box = 12 x (weight of 1 large box) = 12 n
Here, 12 large boxes + 2 small boxes = 249 kilograms
⇒ 2 m+ 12 n = 249 .... (2)
Now, solving both the given equations by ELIMINATION, we get:
5 m + 3 n = 123 x (2)
2 m+ 12 n = 249 x (-5)
we get the new set of equitation as:
10 m + 6 n = 246
- 10 m - 60 n = -1245
Adding both equation, we get
-54 n = 999
or, n = 18.5
Now, 5 m + 3 n = 123
So, 5 m = 123 -3 (18.5) = 123 - 55.5 = 67.5
⇒ m = 13.5
Hence, the weight of a small box = m kg = 13.5 kg
And the weight of 1 large box = n kg = 18.5 kg
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