#### 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.

_____________________ 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.

*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****You Should Also Read:**

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