A florist is organizing a sale that offers carantions at a price of `$4` for 10 and daisies at a price of `$7` for 5. The florist plans to order a maximum of 500 flowers for the sale and wants the revenus from the sale to be at least `$400.` If x is the number of carnations and y is the number of daisies, and the florist sells all the flowers ordered, which system of inequalities best describes this situation ?

Options

A. `0.4x + 1.4y ge 400`
`x +y le 500`
B. ` 0.4x + 1.4y le400`
`x +y le 500`
C. `0.4x + 1.4y ge 400`
`x +y ge 500`
D. `0.4x +1.4yle 400`
`x +y ge 500`

Explanation

To solve the problem, we need to set up a system of inequalities based on the given information about the sale of carnations and daisies.

### Step 1: Define the Variables
Let:
- \( x \) = number of carnations
- \( y \) = number of daisies

### Step 2: Determine the Price per Flower
- The price for 10 carnations is $4, so the price per carnation is:
\[ \text{Price per carnation} = \frac{4}{10} = 0.4 \text{ dollars} \]
- The price for 5 daisies is $7, so the price per daisy is:
\[ \text{Price per daisy} = \frac{7}{5} = 1.4 \text{ dollars} \]

### Step 3: Set Up the Inequalities
1. **Maximum Number of Flowers**: The florist can order a maximum of 500 flowers, which gives us the inequality:
\[ x + y \leq 500 \]

2. **Minimum Revenue Requirement**: The florist wants the revenue from the sale to be at least $400. The revenue from selling \( x \) carnations and \( y \) daisies can be expressed as:
\[ 0.4x + 1.4y \geq 400 \]

### Step 4: Write the System of Inequalities
Combining the two inequalities, we have the system:
\[ \begin{align*} 1. & \quad x + y \leq 500 \\ 2. & \quad 0.4x + 1.4y \geq 400 \end{align*} \]

### Final Answer
The system of inequalities that describes the situation is:
\[ \begin{align*} x + y & \leq 500 \\ 0.4x + 1.4y & \geq 400 \end{align*} \]