Vanessa, a florist, purchases roses for $1.64 each. Her operating expenses are 24% on cost and operating profit is 58% on cost.

a. What is the amount of operating profit on each rose?

Round to the nearest cent

b. What is the selling price of each rose?

Round to the nearest cent. c. What is the rate of markup on selling price?

%

Round to two decimal places

Let's solve the problem step by step.

### Part (a): Operating Profit on Each Rose

Vanessa purchases roses for $1.64 each. The operating profit is 58% of the cost. To find the operating profit per rose:

\[
\text{Operating Profit} = \text{Cost} \times \text{Operating Profit Percentage}
\]

\[
\text{Operating Profit} = 1.64 \times 0.58 = 0.9512
\]

Rounding to the nearest cent:

\[
\text{Operating Profit} \approx \$0.95
\]

### Part (b): Selling Price of Each Rose

The selling price includes the cost, the operating expenses (24% on cost), and the operating profit (58% on cost).

First, let's calculate the operating expenses:

\[
\text{Operating Expenses} = \text{Cost} \times \text{Operating Expenses Percentage}
\]

\[
\text{Operating Expenses} = 1.64 \times 0.24 = 0.3936
\]

Rounding to the nearest cent:

\[
\text{Operating Expenses} \approx \$0.39
\]

Now, the selling price is the sum of the cost, operating expenses, and operating profit:

\[
\text{Selling Price} = \text{Cost} + \text{Operating Expenses} + \text{Operating Profit}
\]

\[
\text{Selling Price} = 1.64 + 0.39 + 0.95 = 2.98
\]

So, the selling price per rose is:

\[
\text{Selling Price} \approx \$2.98
\]

### Part (c): Rate of Markup on Selling Price

The rate of markup is the operating profit as a percentage of the selling price. To find this, we use the formula:

\[
\text{Rate of Markup} = \left(\frac{\text{Operating Profit}}{\text{Selling Price}}\right) \times 100\%
\]

Substituting the values:

\[
\text{Rate of Markup} = \left(\frac{0.95}{2.98}\right) \times 100\% \approx 31.88\%
\]

### Summary of Answers:

a. The operating profit on each rose is **$0.95**.

b. The selling price of each rose is **$2.98**.

c. The rate of markup on selling price is **31.88%**.

Would you like further details or have any questions?

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**Relative Questions:**

1. How would the selling price change if the cost price increased to $2.00?
2. What would be the new operating profit if the operating expenses were reduced to 20% of the cost?
3. If Vanessa wanted to achieve a markup of 40%, what should be the selling price?
4. How would the rate of markup change if the selling price increased to $3.50?
5. What is the impact on the operating profit if the cost price decreases to $1.50?
6. How would the operating expenses affect the selling price if they increased to 30% of the cost?
7. What would be the selling price if the operating profit margin was reduced to 50% of the cost?
8. How does the rate of markup on the selling price compare to the markup on cost?

**Tip:** Always verify your calculations by breaking down the problem into smaller, manageable steps.

Learn how to calculate operating profit, selling price, and markup percentage for Vanessa, a florist who purchases roses at $1.64 each. This problem covers cost and profit analysis, including formulas for operating profit, selling price, and markup percentage. Suitable for adults seeking business calculations.

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