Problem preview

A-CED.3 Warmup M1-003-A02-V04

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

Write a system of inequalities for multiple constraints

Problem

Granola bars cost $\$3$ each and fruit cups cost $\$5$ each. You may spend at most $\$55$ and must buy at least $14~\text{snacks}$. Let $x$ and $y$ be the nonnegative whole-number counts of granola bars and fruit cups. Write a system representing all constraints.

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x + y ≤ 55, 3x + 5y ≥ 14, x ≥ 0, y ≥ 0; x and y are whole numbers

3x + 5y ≥ 55, x + y ≥ 14, x ≥ 0, y ≥ 0; x and y are whole numbers

3x + 5y ≤ 55, x + y ≤ 14, x ≥ 0, y ≥ 0; x and y are whole numbers

3x + 5y ≤ 55, 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