Thursday, April 25, 2024

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box body X and box bottom cover y, then
x + y = 20
2 * 2x = 3Y

x = 60 /7, y = 80 /7

so there are 8 box bodies and 11 box covers. The last one is a box body and a box cover, just forming 17 boxes.

suppose a total of X box bodies and Y box bottoms are made, then
x /2 + Y /3 = 20
one box body and two box bottoms can form a box, then
2 * x = y
solve the binary linear equation, and get
x = 17.14
y = 34.28 (actual rounding)
therefore, the total number of boxes is 17 (16) PCs with 8 white cards, 33 box bottoms with 11 white cards, and 1 box body + 2 box bottoms with the last one (whether it can be cut depends on the actual situation)

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