A certain type of board is sold in lengths of multiples of 2 feet. The shortest board sold is 6 feet, and the longest is 24 feet. A builder needs a large quantity of this type of board in 5 1 2 feet lengths. For minimum waste the lengths to be ordered should be

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Solution

Length of the shortest board = 6 m
Length of the longest board = 24 m
Multiples of 2 are 4, 6, 8, 10, . . . .
This means, we should multiply 5.5m with such number multiples of 2 such that the result must be less than 24m and greater than 6m
So we have the length of board for minimum wastage = 5.5 $\times$ 4 = 22 m

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