Solve using the five "Steps for Solving Applied Problems." A...

Solve using the five "Steps for Solving Applied Problems."
A plumber has a 36 -in. long pipe. He must cut it into two pieces so that one piece is 14 inches longer than the other. How long is each piece?

Key Concepts

Identifying Variables and Defining Unknowns

This concept involves choosing symbols to represent the quantities that are unknown in a problem. It sets the foundation for modeling the problem mathematically by clearly defining what each variable stands for.

Translating Word Problems into Equations

This key concept is about converting the descriptive language and relationships given in a word problem into an algebraic equation. It requires understanding the problem’s narrative and expressing it in a form that can be manipulated using mathematical operations.

Solving Linear Equations

Once an equation is set up, the next step is to apply algebraic techniques to find the value of the unknown variable. This process typically involves combining like terms, isolating the variable, and performing operations that maintain equality.

Interpreting the Solution in Context

After obtaining a numerical solution, it is essential to translate the result back into the context of the original problem. This means checking that the solution makes sense with respect to the problem’s conditions and constraints.

Structured Problem-Solving Approach

This overarching concept emphasizes following systematic steps—from understanding the problem, establishing relationships, performing calculations, to validating results. It ensures that all aspects of the problem are addressed in a logical and organized manner.

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