A 4-ft piece of PVC pipe is cut into three pieces.The longest piece is 12 in. longer than twice

step 1 No 45 there is a pipe which is 4 foot long and so it is 4 feet the length is 4 feet right you ha

A 4-ft piece of PVC pipe is cut into three pieces.The...

Key Concepts

Unit Conversion

Unit conversion involves converting quantities from one measurement unit to another to ensure consistency in calculations. In this context, converting feet to inches is necessary because the problem provides lengths in both feet and inches, and having a single unit throughout simplifies the algebraic process.

Variable Representation

Variable representation is the practice of assigning symbols to unknown quantities. By letting a variable represent the length of one piece, the relationships between the pieces can be expressed algebraically, allowing for systematic problem solving.

Translating Verbal Descriptions into Algebraic Equations

Translating verbal descriptions into algebraic equations is a key skill in solving word problems. This involves interpreting phrases like '12 inches longer than twice the shortest piece' into an algebraic expression, which is essential for modeling the problem mathematically.

Setting Up and Solving Systems of Linear Equations

Setting up and solving systems of linear equations involves creating equations based on the relationships provided in the word problem, then using methods like substitution or elimination to find the values of the variables. This process helps in determining the lengths of all segments from the total available length.

Algebraic Manipulation and Solving for Unknowns

Algebraic manipulation includes combining like terms, isolating variables, and solving equations to determine unknown values. This technique is crucial in systematically reducing the equations to a form that yields a solution, ensuring that all given conditions are satisfied.

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