SOLUTION: A board 18 ft long is cut into two pieces. Two feet less than the product of five and the length of the smaller piece is equal to the difference between three times the length of t

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Question 8616: A board 18 ft long is cut into two pieces. Two feet less than the product of five and the length of the smaller piece is equal to the difference between three times the length of the longer piece and eight. Find the length of each piece.
Here's what I've done and I know I don't have it setup right.
5x-2+x+18
6x=20
x=3 1/3
x+3x+8=18
4x=26
x=6 1/2
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
The way I did it, always start off by identifying the variables:

Let x = length of smaller piece
18-x = length of longer piece

The equation is tricky, but just follow the wording of the sentence that is given:
5(smaller) - 2 = 3(longer) - 8
5(x) - 2 = 3(18-x) - 8
5x - 2 = 54 - 3x - 8
5x - 2 = 46 - 3x

Add 3x to each side:
5x + 3x - 2 = 46 - 3x + 3x
8x - 2 = 46

Add +2 to each side:
8x = 48
x=6 smaller piece
18-x = 12 longer piece

Check:
5(6) -2 = 3(12) - 8
30-2= 36-8
28 = 28
It checks!

R^2 at SCC