Back to Represent constraints with equations — Problem 2 · Task Set 28

Exercises: Represent Constraints with Equations, Inequalities, and Systems

Work through each section in order. For word problems, define your variables before writing any constraint.

Grade 9·20 problems·~40 min·Common Core Math - HS Algebra·standard·hsa-ced-a-3

Work through problems with immediate feedback

Fluency Practice

A nutritionist plans a meal using food X ( $10$ g protein/lb, $2/lb) and food Y ( $5$ g protein/lb, $4/lb). She needs at least 40 g protein and can spend at most $30. Let $x$ = pounds of X and $y$ = pounds of Y. Which system correctly models ALL the constraints, including non-negativity?

$10x + 5y \geq 40$ and $2x + 4y \leq 30$

$10x + 5y \geq 40$ , $2x + 4y \leq 30$ , $x \geq 0$ , $y \geq 0$

$10x + 5y \leq 40$ and $2x + 4y \leq 30$

$10x + 5y = 40$ and $2x + 4y = 30$