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Susan is planting marigolds and impatiens in her garden. Each marigold costs [tex] \$9 [/tex], and each impatien costs [tex] \$7 [/tex]. Susan wants the number of marigolds to be more than twice the number of impatiens. She has a maximum of [tex] \$125 [/tex] to spend on the plants. This situation can be modeled by this system of inequalities:

[tex]
\begin{aligned}
9x + 7y & \leq 125 \\
x & \ \textgreater \ 2y
\end{aligned}
[/tex]

Which statement describes the system of inequalities?

A. The system represents the minimum amount that Susan can spend on impatiens, [tex] x [/tex], and marigolds, [tex] y [/tex], and the relationship between the number of impatiens and marigolds.
B. The system represents the minimum amount that Susan can spend on marigolds, [tex] x [/tex], and impatiens, [tex] y [/tex], and the relationship between the number of marigolds and impatiens.
C. The system represents the maximum amount that Susan can spend on marigolds, [tex] x [/tex], and impatiens, [tex] y [/tex], and the relationship between the number of marigolds and impatiens.
D. The system represents the maximum amount that Susan can spend on impatiens, [tex] x [/tex], and marigolds, [tex] y [/tex], and the relationship between the number of marigolds and impatiens.



Answer :

GinnyAnswer
Sure, let's analyze the given problem step-by-step.

We have:
1. Marigolds cost [tex]$9 each. 2. Impatiens cost $[/tex]7 each.
3. Susan has a budget of $125.
4. The number of marigolds ([tex]\(x\)[/tex]) must be more than twice the number of impatiens ([tex]\(y\)[/tex]).

The situation can be modeled by the system of inequalities:
[tex]\[ \begin{aligned} 9x + 7y &\leq 125 \\ x &> 2y \end{aligned} \][/tex]

Next, let's evaluate the answer choices based on the given constraints:

- Option A: The system represents the minimum amount that Susan can spend on impatiens ([tex]\(x\)[/tex]), and marigolds ([tex]\(y\)[/tex]), and the relationship between the number of impatiens and marigolds.

This statement is incorrect. The inequality [tex]\(9x + 7y \leq 125\)[/tex] represents the maximum amount Susan can spend, not the minimum.

- Option B: The system represents the minimum amount that Susan can spend on marigolds ([tex]\(x\)[/tex]), and impatiens ([tex]\(y\)[/tex]), and the relationship between the number of marigolds and impatiens.

This statement is also incorrect for the same reason as Option A. The inequality [tex]\(9x + 7y \leq 125\)[/tex] represents the maximum amount Susan can spend.

- Option C: The system represents the maximum amount that Susan can spend on marigolds ([tex]\(x\)[/tex]), and impatiens ([tex]\(y\)[/tex]), and the relationship between the number of marigolds and impatiens.

This statement would be correct if the variables [tex]\(x\)[/tex] and [tex]\(y\)[/tex] were reversed. In the inequality [tex]\(9x + 7y \leq 125\)[/tex], [tex]\(x\)[/tex] represents marigolds and [tex]\(y\)[/tex] represents impatiens.

- Option D: The system represents the maximum amount that Susan can spend on impatiens ([tex]\(x\)[/tex]), and marigolds ([tex]\(y\)[/tex]), and the relationship between the number of marigolds and impatiens.

This statement is correct. It accurately describes the inequality [tex]\(9x + 7y \leq 125\)[/tex] as representing the maximum amount Susan can spend on impatiens ([tex]\(x\)[/tex]) and marigolds ([tex]\(y\)[/tex]). It also correctly acknowledges the relationship [tex]\(x > 2y\)[/tex] between the number of marigolds and impatiens.

Hence, the correct answer is D.

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