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

Name: Problem 17, Chapter 3: Beginning and Intermediate Algebra
Uploaded: 2020-06-30T16:45:45-08:00
Duration: 1 min 33 s
Channel: Peter Winans
Description: Solve using the five "Steps for Solving Applied Problems." Calida's mom found an 18 -ft-long rope in the garage. She will cut it into two pieces so that one piece can be used for a long jump rope and the other for a short one. If the long rope is to be twice as long as the short one, find the length of each jump rope.

Solve using the five "Steps for Solving Applied Problems." Calida's mom found an 18 -ft-long rope in the garage. She will cut it into two pieces so that one piece can be used for a long jump rope and the other for a short one. If the long rope is to be twice as long as the short one, find the length of each jump rope.

Solve using the five "Steps for Solving Applied Problems."
Calida's mom found an 18 -ft-long rope in the garage. She will cut it into two pieces so that one piece can be used for a long jump rope and the other for a short one. If the long rope is to be twice as long as the short one, find the length of each jump rope.

Key Concepts

Problem Solving Strategies

The five steps for solving applied problems provide a strategic framework to tackle real-world problems. These steps usually include understanding the problem, devising a plan, carrying out the plan, checking the work, and communicating the solution. This methodical approach helps in breaking down complex tasks into simpler, manageable parts.

Algebraic Modeling

Algebraic modeling is the process of converting a real-world situation into a mathematical form. It involves interpreting the given information and translating it into variables, equations, or expressions that reflect the relationships and constraints described in the problem.

Variable Assignment

Variable assignment is a key concept where unknown quantities in a problem are represented by symbols. Assigning variables allows the relationships between different elements of the problem to be expressed in a precise and general form, which is essential for building equations.

Equation Formation and Solving

Once variables have been assigned, the next step is to form an equation that reflects the relationship between these variables based on the problem's conditions. Solving this equation using algebraic techniques yields the values of the unknown quantities, thereby providing the solution to the problem.

Proportional Reasoning

Proportional reasoning involves understanding and applying the concept of ratios and multiples in a problem. In situations where one quantity is a multiple of another, such as when one segment is twice the length of another, proportional reasoning is used to establish a linear relationship that can be solved through algebraic methods.

Transcript

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