A fruit company delivers its fruit in two types of boxes: large and small. A delivery of 8 large boxes and 3 small boxes has a total weight of 187 kilograms. A delivery of 2 large boxes and 5 small boxes has a total weight of 102 kilograms. How much does each type of box weigh?

Weight of large box = 18.5 Kg

Weight of small box = 13 Kg

Step-by-step explanation:

Let the weight of large box be X kg

Let the weight of small box be Y kg

So weight of 8 large boxes = 8X

weight of 3 small box be =  3Y

According to question

8 large boxes and 3 small boxes has a total weight of 187

mathematically it can be represented as

8X + 3 Y = 187

Second condition

weight of 2 large boxes = 2X

weight of 5 small box be =  5Y

According to question

2 large boxes and 5 small boxes has a total weight of 102 kilograms

mathematically it can be represented as

2X + 5Y = 102

we have two equation

8X + 3 Y = 187   A

2X + 5Y = 102   B

multiplying equation B with 4  on both side of equation we have

4*(2X + 5Y) = 4*102

=> 8X + 20Y = 408   C

Now subtracting equation A and C on both sides we have

8X + 3 Y - (8X + 20Y ) = 187 -408

8X - 8X + 3 Y -  20Y = -221

-17Y = -221

=> Y = -221/-17 = 13

Now substituting value of Y in equation B we have

2X + 5*13 = 102

=> 2X + 65 = 102

=> X = (102-65)/2  = 18.5

Weight of large box = 18.5 Kg

Weight of small box = 13 Kg

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explanation:

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step-by-step explanation: