Answer :
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.
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.
