The height of a plant is controlled by three genes. The maximum height in the species is 24 inches , wherease the minimum height in the species is 6 inches . What would be the height of a plant of the same species whose genotype in AaBBcc?

Options

A. 12 inches
B. 15 inches
C. 18 inches
D. 21 inches

Answer

To solve the problem of determining the height of a plant with the genotype AaBBcc, we will follow these steps:

### Step-by-Step Solution:

1. **Identify Maximum and Minimum Heights**:
- The maximum height of the plant species is 24 inches.
- The minimum height of the plant species is 6 inches.

2. **Calculate the Range of Height**:
- The range of height is calculated by subtracting the minimum height from the maximum height:
\[ \text{Range} = \text{Maximum Height} - \text{Minimum Height} = 24 \text{ inches} - 6 \text{ inches} = 18 \text{ inches} \]

3. **Determine the Number of Genes**:
- The height of the plant is controlled by 3 genes (let's denote them as A, B, and C).

4. **Calculate the Contribution of Each Gene**:
- To find the contribution of each gene, divide the range of height by the number of genes:
\[ \text{Contribution per gene} = \frac{\text{Range}}{\text{Number of Genes}} = \frac{18 \text{ inches}}{3} = 6 \text{ inches} \]

5. **Identify the Dominant Alleles in the Genotype**:
- The genotype provided is AaBBcc. Here, 'A' and 'B' are dominant alleles while 'c' is recessive.
- Therefore, we have 2 dominant alleles (A and B) and 1 recessive allele (c).

6. **Calculate the Contribution of Dominant Alleles**:
- Each dominant allele contributes 6 inches to the height. Since we have 2 dominant alleles (A and B):
\[ \text{Total contribution from dominant alleles} = 2 \times 6 \text{ inches} = 12 \text{ inches} \]

7. **Calculate the Final Height of the Plant**:
- Now, add the minimum height to the total contribution from the dominant alleles:
\[ \text{Height of the plant} = \text{Minimum Height} + \text{Contribution from Dominant Alleles} = 6 \text{ inches} + 12 \text{ inches} = 18 \text{ inches} \]

### Final Answer:
The height of the plant with the genotype AaBBcc would be **18 inches**.