Modeling with Equation/InequalityConstraints Practice Test

A community garden is planting tomatoes and peppers. Let $x$ = number of tomato plants and $y$ = number of pepper plants.

Constraints:

• There is space for at most 30 plants total: $x+y\le 30$.
• Tomato plants must be at least 10: $x\ge 10$.
• Each tomato plant needs 2 minutes/day of watering and each pepper plant needs 3 minutes/day; they have at most 75 minutes/day: $2x+3y\le 75$.
• $x$ and $y$ must be nonnegative whole numbers.

Is the point $(12, 6)$ a viable solution? Explain by identifying whether it satisfies all constraints.

A school club is buying snacks for an event. Let $x$ be the number of boxes of granola bars and $y$ be the number of boxes of fruit snacks. Each granola bar box costs $\$6$ and each fruit snack box costs $$4$. The club has at most $\$60$ to spend and needs at least 12 total boxes. Also, $x$ and $y$ cannot be negative.

Which system of inequalities models these constraints?