To solve this problem, let's break down the information given and determine the correct equation.

Problem Breakdown

1. Cost of Roses: Each rose costs $3.50, and there are $x$ roses.

   • Total cost for roses: $3.50x$.

2. Cost of Carnations: Each carnation costs $2.25, and there are 10 carnations.

   • Total cost for carnations: $2.25 \times 10 = 22.5$.

3. Average Cost Requirement: The average cost per flower in the bouquet should be $3.00.

   • Total number of flowers is $x + 10$ (roses and carnations combined).
   • The total cost of all flowers divided by the total number of flowers should equal $3.00.

Setting Up the Equation

The average cost can be expressed as: $\frac{3.50x + 22.5}{x + 10} = 3$

Now, let’s multiply both sides by $x + 10$ to eliminate the denominator: $3.50x + 22.5 = 3(x + 10)$

This matches Option A: $3.50x + 2.25(10) = 3(x + 10)$

Conclusion

The correct answer is Option A.

Would you like further explanation on any steps?

Additional Questions

1. How would the equation change if the average price per flower were different?
2. What if the number of carnations were different—how would that affect the equation?
3. Can we solve for $x$ to find the exact number of roses needed?
4. How does multiplying by $x + 10$ help in simplifying the equation?
5. Why do we equate the total cost to an average cost of $3 per flower?

Tip

When dealing with average costs, remember to set up an equation dividing the total cost by the total quantity and set it equal to the desired average value.