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Dissection of a Word Problem


Let's break the following word problem into several pieces in order to solve it. The paragraph will be repeated with a phrase highlighted in red. The explanation will follow below the paragraph.

A 12 foot piece of string is cut into 2 pieces so that the longer piece is 3 feet longer than twice the shorter piece. If the shorter piece is X feet long, find the lengths of both pieces.



A 12 foot piece of string is cut into 2 pieces so that the longer piece is 3 feet longer than twice the shorter piece. If the shorter piece is X feet long, find the lengths of both pieces.


_____________________ This string is 12 ft long.



A 12 foot piece of string is cut into 2 pieces so that the longer piece is 3 feet longer than twice the shorter piece. If the shorter piece is X feet long, find the lengths of both pieces.


Let's cut the string into two pieces.

________ plus _________________ = 12 feet.
short piece.................long piece



A 12 foot piece of string is cut into 2 pieces so that the longer piece is 3 feet longer than twice the shorter piece. If the shorter piece is X feet long, find the lengths of both pieces.


The shorter piece is X feet long :

________

X(ft) long



A 12 foot piece of string is cut into 2 pieces so that the longer piece is 3 feet longer than twice the shorter piece. If the shorter piece is X feet long, find the lengths of both pieces.


the longer piece is 3 feet longer
_________________
+ 3



A 12 foot piece of string is cut into 2 pieces so that the longer piece is 3 feet longer than twice the shorter piece. If the shorter piece is X feet long, find the lengths of both pieces.


3 feet longer than what? 3 feet longer than twice the shorter piece.
_________________

longer piece: 2X + 3


A 12 foot piece of string is cut into 2 pieces so that the longer piece is 3 feet longer than twice the shorter piece. If the shorter piece is X feet long, find the lengths of both pieces.


REMEMBER:
________ plus _________________ = 12 feet.
short piece + long piece



THUS:
________ plus _________________ = 12
(x)feet + 2X + 3 = 12



Set up the equation and solve as below -
X + 2X + 3 = 12
3X + 3 = 12 (combined liked terms)
3X + 3 - 3 = 12 - 3 (subtracted 3 from both sides)
3X = 9
3X/3 = 9/3 (divide both sides by 3)
X = 3




Since "X" represented the length of the shorter piece. The shorter piece is 3 feet long.
"2X +3" represented the length of the longer piece. Thus, the longer piece is calculated by substituting 3 in place of X and solve. 2(3) + 3 = 9 The longer piece of string is 9 ft long.
In summary: short piece = 3 ft; long piece = 9ft




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Content copyright © 2014 by Beverly Mackie. All rights reserved.
This content was written by Beverly Mackie. If you wish to use this content in any manner, you need written permission. Contact Beverly Mackie for details.

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