A student observed 34 inflorescences in Bougainvillea and 42 inflorescences in Poinsettia. Find out the number of flowers in Bougainvillea and the number of female flower in Poinsettia, respectively

Options

A. 34,126
B. 204.164
C. 102,42
D. 68 indefinite.

Answer

To solve the problem, we need to find the number of flowers in Bougainvillea and the number of female flowers in Poinsettia based on the given inflorescence counts.

### Step-by-Step Solution:

1. **Understanding Bougainvillea Inflorescence:**
- The inflorescence in Bougainvillea is a type called "simple cyme" or "symole."
- In this type of inflorescence, the peduncle (the stalk that supports the flower) ends in a flower, and it produces two lateral branches, each ending in a flower.
- Therefore, each inflorescence typically has 3 flowers.

2. **Calculating Total Flowers in Bougainvillea:**
- The student observed 34 inflorescences in Bougainvillea.
- To find the total number of flowers, we multiply the number of inflorescences by the number of flowers per inflorescence:
\[ \text{Total Flowers in Bougainvillea} = 34 \text{ inflorescences} \times 3 \text{ flowers per inflorescence} = 102 \text{ flowers} \]

3. **Understanding Poinsettia Inflorescence:**
- The inflorescence in Poinsettia is called "cyathium."
- In a cyathium, there is a single female flower surrounded by multiple male flowers.
- The single female flower in Poinsettia is tricarpellary, meaning it has three carpels.

4. **Calculating Number of Female Flowers in Poinsettia:**
- The student observed 42 inflorescences in Poinsettia.
- Since each cyathium contains one female flower, the total number of female flowers is equal to the number of inflorescences:
\[ \text{Total Female Flowers in Poinsettia} = 42 \text{ inflorescences} \times 1 \text{ female flower per inflorescence} = 42 \text{ female flowers} \]

5. **Final Results:**
- The number of flowers in Bougainvillea is 102.
- The number of female flowers in Poinsettia is 42.

### Summary:
- **Bougainvillea:** 102 flowers
- **Poinsettia:** 42 female flowers