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?

A) 3x + 2y < 30.
B) 3x + 2y < 30.
C) 2x + 3y > 30.
D) 2x + 3y < 30.

Answer 1

The correct inequality to represent the combinations of roses and carnations that a student can buy without exceeding a $30 budget is 3x + 2y ≤ 30.

Step-by-step explanation:

The question seeks to determine which inequality correctly represents the scenario where a student is shopping for a flower arrangement consisting of roses and carnations with a budget of up to $30. Roses cost $3 each and carnations cost $2 each. The total cost for x roses and y carnations should not exceed $30, which leads to the inequality 3x + 2y ≤ 30. Thus, the correct option would be:

A) 3x + 2y ≤ 30.

This inequality must be inclusive, which means it should include the possibility of spending exactly $30, hence the use of the ≤ (less than or equal) rather than just < (less than).