Question

audrey has \\(x\\) pounds of red grapes and \\(y\\) pounds of green grapes. she has less than 5 pounds of grapes in all.

which are reasonable solutions for this situation?
check all that apply.

\\((-1, 2)\\)
\\((1, 3.5)\\)
\\((2, 2)\\)
\\((4.5, 0.5)\\)
\\((5, 0)\\)

Explanation:

Formulate the inequality

We represent the total weight of grapes.
Using the Linear Inequalities knowledge point:
Audrey has \(x\) pounds of red grapes and \(y\) pounds of green grapes.
She has less than 5 pounds of grapes in total:

$$x + y < 5$$

Identify real-world constraints

We apply physical constraints to the variables.
Since weight cannot be negative, we must have:

$$x \ge 0 \quad \text{and} \quad y \ge 0$$

Test the given options

We evaluate each coordinate pair against all constraints.

• For \((-1, 2)\):

\(x = -1\), which is negative. This is not reasonable.

• For \((1, 3.5)\):

\(x = 1 \ge 0\), \(y = 3.5 \ge 0\).
\(1 + 3.5 = 4.5 < 5\). This is reasonable.

• For \((2, 2)\):

\(x = 2 \ge 0\), \(y = 2 \ge 0\).
\(2 + 2 = 4 < 5\). This is reasonable.

• For \((4.5, 0.5)\):

\(x = 4.5 \ge 0\), \(y = 0.5 \ge 0\).
\(4.5 + 0.5 = 5\), which is not strictly less than 5. This is not reasonable.

• For \((5, 0)\):

\(x = 5 \ge 0\), \(y = 0 \ge 0\).
\(5 + 0 = 5\), which is not strictly less than 5. This is not reasonable.

Answer:

• ☐ \((-1, 2)\)
• ☑ \((1, 3.5)\) (Correct answer)
• ☑ \((2, 2)\) (Correct answer)
• ☐ \((4.5, 0.5)\)
• ☐ \((5, 0)\)