Problem preview

A-CED.3 Warmup M1-003-A02-V03

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

Write a system of inequalities for multiple constraints

Problem

Sandwiches sell for $\$4$ each and salads for $\$6$ each. You must earn at least $\$48$ while selling at most $14~\text{items}$. Let $x$ and $y$ be the nonnegative whole-number counts of sandwiches and salads. Write a system representing all constraints.

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4x + 6y ≥ 48, x + y ≤ 14, x ≥ 0, y ≥ 0; x and y are whole numbers

x + y ≥ 48, 4x + 6y ≤ 14, x ≥ 0, y ≥ 0; x and y are whole numbers

4x + 6y ≥ 48, x + y ≥ 14, x ≥ 0, y ≥ 0; x and y are whole numbers

4x + 6y ≤ 48, x + y ≤ 14, x ≥ 0, y ≥ 0; x and y are whole numbers

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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: Write a system of inequalities for multiple constraints