Medical residents at Lakewood Hospital are choosing their individual specialties. Among them, 40% choose cardiology, 16% choose oncology, 34% choose endocrinology, and the remaining x% choose hematology. Once the doctors pick their first speciality , they are then each asked to choose a second specialty from the previous four options in case their original speciality is already filled. They may not pick their original speicality again. 20% of those who originally picked cardiology choose oncology as their second choice. IF no other field choose oncology as their second choice, and the hospitals boasts 200 medical residents, then what is the total number of residents who named oncology as either their first or second choice, in terms of x?

Options

A. 8x-128
B. 8x-144
C. `x^2+24x-188`
D. `x^2-24x+188`

Answer

To solve the problem step by step, we will break down the information provided and calculate the required values systematically.

### Step 1: Determine the number of residents choosing each specialty

Given:
- Total number of medical residents = 200
- Percentage choosing cardiology = 40%
- Percentage choosing oncology = 16%
- Percentage choosing endocrinology = 34%
- Percentage choosing hematology = x%

First, we calculate the number of residents for each specialty:

1. **Cardiology**:
\[ \text{Number choosing cardiology} = 40\% \text{ of } 200 = \frac{40}{100} \times 200 = 80 \]

2. **Oncology**:
\[ \text{Number choosing oncology} = 16\% \text{ of } 200 = \frac{16}{100} \times 200 = 32 \]

3. **Endocrinology**:
\[ \text{Number choosing endocrinology} = 34\% \text{ of } 200 = \frac{34}{100} \times 200 = 68 \]

4. **Hematology**:
\[ \text{Percentage of residents choosing hematology} = x\% \]
To find x, we use the fact that the total percentage must equal 100%:
\[ x = 100 - (40 + 16 + 34) = 100 - 90 = 10\% \]

### Step 2: Calculate the number of residents choosing hematology
Now we can calculate the number of residents choosing hematology:
\[ \text{Number choosing hematology} = 10\% \text{ of } 200 = \frac{10}{100} \times 200 = 20 \]

### Step 3: Determine the second choice for oncology
According to the problem, 20% of those who chose cardiology select oncology as their second choice. Therefore, we calculate:
\[ \text{Number choosing oncology as second choice} = 20\% \text{ of } 80 = \frac{20}{100} \times 80 = 16 \]

### Step 4: Calculate the total number of residents who named oncology
Now we can find the total number of residents who named oncology as either their first or second choice:
\[ \text{Total choosing oncology} = \text{First choice} + \text{Second choice} = 32 + 16 = 48 \]

### Final Answer
The total number of residents who named oncology as either their first or second choice is **48**.

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