Question

james wants to buy roses and daisies for his grandmother. the local florist is having a sale. roses only cost $2 and daisies cost $1. james wants to spend at least $11. given x represents the number of roses and y represents the number of daisies, look at the graph below. james wants to buy no more than 20 roses and daisies. complete the statement to indicate which section of the graph represents the solution to this system of inequalities.

Explanation:

Step1: Define inequalities

Let $x$ = number of roses, $y$ = number of daisies.

1. Cost constraint: $2x + y \geq 11$
2. Total quantity constraint: $x + y \leq 10$
3. Non-negativity: $x \geq 0, y \geq 0$

Step2: Graph boundary lines

• For $2x + y = 11$: intercepts at $(5.5, 0)$ and $(0, 11)$; shade above the line (since $\geq$).
• For $x + y = 10$: intercepts at $(10, 0)$ and $(0, 10)$; shade below the line (since $\leq$).

Step3: Find overlapping region

The valid region is where both shaded areas overlap, which is section B.

Answer:

Section B