SOLUTION: a 33 inch wooden board is cut into two pieces. The longer piece is 3 inches less than twice the other piece. find the shorter piece. when 10 is added to one-third of a number, t

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Question 202956: a 33 inch wooden board is cut into two pieces. The longer piece is 3 inches less than twice the other piece. find the shorter piece.
when 10 is added to one-third of a number, the result is the same as if eight had been subtracted from twice the number.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
1. Let a be the length of the shorter piece and b = the length of the longer piece.
a+b = 33
b = 2a-3 Substitute this into the first equation.
a+(2a-3) = 33 Solve for a.
3a-3 = 33 Add 3 to both sides.
3a = 36 Divide both sides by 3.
a = 12
The shorter piece is 12 inches long.
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Let n be the missing number, then:
%281%2F3%29n%2B10+=+2n-8 Multiply through by 3.
n%2B30+=+6n-24 Subtract n from both sides.
30+=+5n-24 Add 24 to both sides.
54+=+5n Divide both sides by 5.
highlight%28n+=+10.8%29