Fraction word problem

Question

You have been given the job of cutting a supply of 2" × 4" pieces of lumber for a frame house. Each piece is to be 14 ½ inches long. Each cut is 1/8 inch wide. At Home Depot and Lowe’s, the choices of stock length are 10 feet, 12 feet, and 14 feet. You have been asked to choose the length of stock that will have the least amount of waste after you cut as many pieces as you can from it. 

Which length of stock should you choose?

Answer 1

10 feet = 120 inches

120 divided by 14.5 is 8 cuts;

the blade eats 1/8*8 = 1 inch

120 - (14.5*8 + 1) = 120 - 117 = 3 inches wasted

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12 feet = 240 inches

240 divided by 14.5 = 16 cuts;

the blade eats 1/8*16 = 2 inches

240 - (14.5*16 + 2) = 240 - 234 = 6 inches wasted

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14 feet = 280 inches

280 divided by 14.5 = 19 cuts

the blade wats 1/8*19 = 19/8 = 2.375 inches

280 - (19*14.5 + 2.375) = 277.875 = 2.125 inches wasted

so purchase the 14 foot long 2 by 4s