A three-foot-long deli sandwich must be split into three...

Name: Problem 44, Chapter 7: Beginning and Intermediate Algebra
Uploaded: 2022-02-16T23:06:17-08:00
Duration: 1 min 45 s
Channel: Rylie Howey
Description: A three-foot-long deli sandwich must be split into three pieces so that the middle piece is twice as long as the shortest piece and the shortest piece is 8 in. shorter than the longest piece. How long should the three pieces be?

A three-foot-long deli sandwich must be split into three pieces so that the middle piece is twice as long as the shortest piece and the shortest piece is 8 in. shorter than the longest piece. How long should the three pieces be?

Key Concepts

System of Linear Equations

A system of linear equations involves multiple equations that share common variables and must be solved simultaneously. This concept is crucial for solving problems where several conditions interact, as it allows one to find the unique values of the unknowns that satisfy all the given conditions.

Unit Conversion

Unit conversion is the process of translating measurements from one unit to another to maintain consistency within a problem. It is particularly important in problems where the units of measurement provided (such as feet) differ from the units required for some conditions (such as inches), ensuring all equations are correctly balanced.

Translating Word Problems into Equations

This key concept refers to the process of expressing the relationships and conditions described in a narrative as algebraic equations. It requires identifying the relationships between the unknowns, such as comparative lengths or differences, and accurately reflecting those relationships in mathematical form.

Variable Assignment

This concept involves designating symbols, usually letters, to represent unknown quantities in a problem. In word problems, assigning variables is the first step in turning a verbal description into a mathematical model, allowing for the systematic formulation and manipulation of equations to find solutions.

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