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Answer :
By setting up a system of linear equations from the deliveries data, we can solve for the weight of each box type. The large box weighs 18.25 kg and the small box weighs 15.25 kg.
To solve for the weight of each type of box, we can set up a system of linear equations based on the given deliveries. Let L represent the weight of a large box and S represent the weight of a small box. We have two deliveries that give us two equations:
- 5L + 3S = 137 kg (from the delivery of five large boxes and three small boxes)
- 2L + 6S = 128 kg (from the delivery of two large boxes and six small boxes)
By solving this system of equations, we find the weight of each box type. Let's multiply the second equation by 2.5 to match the coefficient of L's in the first equation:
- 5L + 3S = 137
- 5L + 15S = 320 (after multiplying the second equation by 2.5)
To eliminate L, we subtract the first equation from the second:
12S = 183
Dividing both sides by 12:
S = 183 / 12
S = 15.25 kg
Now we substitute S back into the first equation to solve for L:
5L + 3(15.25) = 137
5L + 45.75 = 137
5L = 137 - 45.75
5L = 91.25
L = 91.25 / 5
L = 18.25 kg
The large box weighs 18.25 kg and the small box weighs 15.25 kg.
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