Problem preview

A-CED.3 Warmup M1-003-A06-V03

Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.

Interpret a boundary point in context

Problem

For \(4x+6y\le~32\), \(x\) counts \(4\text{-}\text{inch}\) wood pieces and \(y\) counts \(6\text{-}\text{inch}\) metal pieces. Interpret boundary point \((5,2)\) using both quantities, inches used, and material-limit status.

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wood pieces = 5; metal pieces = 2; material used = 7 inches; limit status = below limit

wood pieces = 5; metal pieces = 2; material used = 32 inches; limit status = exactly reaches limit

wood pieces = 2; metal pieces = 5; material used = 38 inches; limit status = exceeds limit

wood pieces = 5; metal pieces = 2; material used = 32 inches; limit status = not allowed at equality

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Curriculum context

Course: Math I
Standard: A-CED.3
Category: Algebra
Domain: Creating Equations
Objective: Represent constraints with equations, inequalities, and systems; interpret viable and non-viable solutions in context.
Problem type: Interpret a boundary point in context