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# Help?

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Jon has 3 boards that are each 8 feet long.  First he makes 3 identical shelves.  Then he uses 18 inches to make a bird house.  When finished, he has 25% of the original amount left.  How much wood was used for each shelf, in feet?

Jan 17, 2018

#1
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Jon has 3 boards that are each 8 feet long.  First he makes 3 identical shelves.  Then he uses 18 inches to make a bird house.  When finished, he has 25% of the original amount left.  How much wood was used for each shelf, in feet?

3 x 8 =24 feet - That Jon started with.

25% x 24 = 6 feet left.

24 - 6 = 18 feet used to make 3 shelves and a bird house

18 inches / 12 = 1.5 feet used for the bird house.

18 - 1.5 = 16.5 feet used for the 3 shelves

16.5 / 3 = 5.5 feet used for each of the 3 shelves.

Jan 17, 2018
#2
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Another approach....let x be the length of each shelf   and let 18 in  =

18/12 ft  = 3/2  ft =  1.5 ft

So we have

[ 3* 8   -  1.5  -  3x ]  =  .25  [ 3*8]     simplify

[ 24  -  1.5 - 3x ]  =  .25 * 24

22.5 - 3x  =   8         add 3 to each side, subtract 8 from both sides

22.5 - 8  = 3x

16.5  =  3x       divide both sides by 3

5.5  =  x   ⇒      5.5 ft  = the length of each shelf

Jan 17, 2018