Answer :
Final answer:
To solve this problem, let's assign variables to the weight of the large box and the weight of the small box. We can solve this system of equations using either substitution or elimination. The weight of the large box is 18.25 kilograms and the weight of the small box is 15.5 kilograms.
Explanation:
To solve this problem, let's assign variables to the weight of the large box and the weight of the small box. Let's say the weight of the large box is L and the weight of the small box is S. We can then set up a system of equations to represent the given information:
2L + 3S = 83
4L + 8S = 197
We can solve this system of equations using either substitution or elimination. I'll use the elimination method:
Multiplying the first equation by 4 and the second equation by 2, we get:
8L + 12S = 332
8L + 16S = 394
Subtracting the first equation from the second equation, we get:
4S = 62
Dividing both sides by 4, we find that S = 15.5.
Substituting this value of S back into the first equation, we can solve for L:
2L + 3(15.5) = 83
2L + 46.5 = 83
2L = 36.5
L = 18.25
So, the weight of the large box is 18.25 kilograms and the weight of the small box is 15.5 kilograms.
Complete Question:
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 2 large boxes and 3 small boxes has a total weight of 83 kilograms. A delivery of 4 large boxes and 8 small boxes has a total weight of 197 kilograms. How much does each type of box weight.
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