Question

a student is ordering a flower arrangement. she can choose any combination of roses and carnations for her flower arrangement, and she does not want to spend more than $30. if roses cost $3 each and carnations cost $2 each, which inequality represents all possible combinations of x roses and y carnations? 3x + 2y < 30 2x + 3y ≤ 30 3x + 2y ≤ 30 2x + 3y > 30

Explanation:

Step1: Calculate the cost of roses and carnations

The cost of \(x\) roses at \(\$3\) each is \(3x\) dollars. The cost of \(y\) carnations at \(\$2\) each is \(2y\) dollars. The total cost of the flower arrangement is \(3x + 2y\) dollars.

Step2: Set up the inequality based on the budget

The student does not want to spend more than \(\$30\). The phrase “not more than” means “less than or equal to”. So the inequality is \(3x+2y\leq30\).

Answer:

\(3x + 2y\leq30\) (the third option)