SOLUTION: A 9ft board was cut into 2 pieces so that one piece is 5 feet longer than 3 times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.

Question 54964: A 9ft board was cut into 2 pieces so that one piece is 5 feet longer than 3 times the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces.
Found 2 solutions by psbhowmick, tutorcecilia:
Answer by psbhowmick(878) (Show Source): You can put this solution on YOUR website!
Shorter piece = x feet.
Three times the shorter piece = 3x feet.
Longer piece = (3x + 5) feet.
Now, total length = Shorter piece + Longer piece.
So, 9 = x + (3x + 5)
or 9 = 4x + 5
or x = 1
So longer piece is (3x + 5) = 8 feet and shorter piece is x = 1 foot.
Answer by tutorcecilia(2152) (Show Source): You can put this solution on YOUR website!
A 9ft board was cut into 2 pieces
Translation:
Piece #1 + Piece # 2 = 9 ft
.
Piece # 1 = one piece is 5 feet longer than 3 times
translation: Piece # 1 = (3x+5)
.
Piece # 2= the shorter piece
Translation: (x)
.
So,
Piece #1 + Piece # 2 = 9 ft
(3x+5)+(x)=9
3x+5+x=9 [Simplify]
4x+5=9 [Solve for x]
4x+5-5=9-5
4x=4
4x/4=4/4
x=1ft (Length of Piece #2)
.
Check by plugging the values back into the original equation:
Piece #1 + Piece # 2 = 9 ft
(3x+5)+(x)=9
(3(1)+5)+(1)=9
3+5+1=9
9=9 [Checks out]

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