Fred Willianson had some leftover boards that were 16 feet long. He decided to use them for projects in his house. First he cut a 16 foot board into two unequal pieces. He then cut five additional 16 foot boards using exactly the same dimensions. He used all six of the longer pieces to complete a wall. He used four of the shorter pieces to case in a stairwell. In all, he used 82 linear feet of boards on the two projects. What were the lengths of the pieces after he cut each baord in two?
2006-11-04 13:28:08 · 8 answers · asked by colostomybag4fun1 2 in Science & Mathematics ➔ Mathematics
The most important thing in any word problem is figuring out how to set it up. Our intrepid builder cut a total of 6 boards, and used the longer pieces from all of them, so he used 6x feet of wood. Additionally, he used 4 of the smaller pieces, each of which is (16 - x) feet long. This accounts for another 4(16 - x) feet. This all has to add up to 82 feet of boards, so we get the equation:
6x + 4(16 - x) = 82
This simplifies as follows:
6x + 64 - 4x = 82
2x + 64= 82
The final answer is left as an exercise for the reader.
2006-11-04 13:35:41 · answer #1 · answered by Joseph Q 2 · 2⤊ 1⤋
Six 16 foot boards is 96 total feet, but only 82 feet were used, and two equal pieces were NOT used, so subtract 82 from 96 then divide by 2 to get the unused (shorter) piece. Then you can easily find the longer piece.
2006-11-04 13:38:24 · answer #2 · answered by hayharbr 7 · 0⤊ 1⤋
First of all, guy above me is wrong because if it were 8ft, there wouldnt be a longer board or a shorter board, they would be equal. The correct answer is..
2sp=14ft so if the 2 short pieces account for 14 feet... then 1 piece= 7ft. Therefore the answer is SP=7ft and LP=9ft. So...we know there was a 16 foot board that was cut into 2 pieces..one of the pieces was 7 ft long..so if you cut off a 7 foot long piece of wood.. off of a 16 foot piece of wood..then the other (Long piece) is 9ft. Therefore the two lengths of the pieces after he cut each board in two is 7ft and 9ft.
2006-11-04 13:58:02 · answer #3 · answered by C.J. W 3 · 0⤊ 1⤋
S + L = 16
6L + 4S = 82
L=9, S = 7
2006-11-04 13:37:14 · answer #4 · answered by just♪wondering 7 · 1⤊ 0⤋
8 feet
2006-11-04 13:33:28 · answer #5 · answered by J 6 · 0⤊ 2⤋
8 feet
2006-11-04 13:29:49 · answer #6 · answered by guy 1 · 0⤊ 2⤋
Two equations with two unknowns:
L + S = 16
6L + 4S = 82
2006-11-04 13:33:41 · answer #7 · answered by arbiter007 6 · 0⤊ 1⤋
toughness.
2006-11-04 13:29:40 · answer #8 · answered by Anonymous · 0⤊ 2⤋