Answered

Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Select the correct answer.

Susan is planting marigolds and impatiens in her garden. Each marigold costs [tex]$\$[/tex] 9[tex]$, and each impatien costs $[/tex]\[tex]$ 7$[/tex]. Susan wants the number of marigolds to be more than twice the number of impatiens. She has a maximum of [tex]$\$[/tex] 125$ 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 marigolds, [tex]$x$[/tex], and impatiens, [tex]$y$[/tex], and the relationship between the number of marigolds and impatiens.

B. 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.

C. 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.

D. 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.

Sagot :

GinnyAnswer
Let's break down the given system of inequalities:

1. \( 9x + 7y \leq 125 \):
- This inequality represents the constraint on the total cost of the marigolds (denoted by \( x \)) and impatiens (denoted by \( y \)). Each marigold costs \( \[tex]$9 \) and each impatien costs \( \$[/tex]7 \). The total amount Susan can spend on these plants should not exceed \( \$125 \).

2. \( x > 2y \):
- This inequality represents the relationship between the number of marigolds (\( x \)) and the number of impatiens (\( y \)). Specifically, the number of marigolds should be more than twice the number of impatiens.

The correct statement needs to encapsulate these interpretations:

- \( 9x + 7y \leq 125 \) describes the maximum amount Susan can spend on marigolds and impatiens.
- \( x > 2y \) describes the relationship that the number of marigolds should be more than twice the number of impatiens.

Therefore, comparing all the given options:

A. This statement mentions the minimum amount spent, which is incorrect because the inequality indicates a maximum spending limit.

B. This statement correctly identifies the system of inequalities as representing the maximum amount that Susan can spend on marigolds (\( x \)) and impatiens (\( y \)), and correctly describes the relationship between the number of marigolds and impatiens.

C. This statement switches the variables \( x \) and \( y \), incorrectly identifying impatiens as \( x \) and marigolds as \( y \).

D. This statement incorrectly describes the inequalities in terms of minimum spending.

The correct answer is:
B. 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.
Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.