SOLUTION: A 21 ft board is cut into two pieces. The shorter piece is 5 ft than the longer piece . What is the length of the longer piece?

Question 596089: A 21 ft board is cut into two pieces. The shorter piece is 5 ft than the longer piece . What is the length of the longer piece?
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
A 21 ft board is cut into two pieces. The shorter piece is 5 ft than the longer piece . What is the length of the longer piece?
Hi, there--
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One way to solve this problem is to experiment with pairs of numbers that are 5 feet apart until you find two that add up to 21 feet. This works, but it can be time consuming.
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Here is a method using algebra:
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Let's have x be the length of the shorter piece.
The other piece is feet longer, In algebra, we write that as x+5.
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Now we make an equation. The two lengths add up to 21 feet, so

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Simplify and solve for x.

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Subtract 5 from both sides of the equation.

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If 2x is 16, then x must be 8. The shorter length is 8 feet. To find the other length, we subtract 21 - 8 = 13. The longer piece is 13 feet.
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CHECK:
1) Do two pieces add up to 21 feet? 8+13=21...YES!
2) Is one piece 5 feet longer than the other? 13-8=5...BINGO!
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Hope this helps! Email with any questions.
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Ms.Figgy
math.in.the.vortex@gmail.com

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