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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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