To determine the total number of registered doctors given that 23.3% of them were female and that there were 57,700 female registered doctors, we can proceed with the following steps:
1. Understand the relationship:
[tex]\[
\text{Percentage of Female Doctors} = \frac{\text{Number of Female Doctors}}{\text{Total Number of Doctors}} \times 100
\][/tex]
2. Substitute the known values:
Given that 23.3% of the doctors are female and there are 57,700 female doctors, we can write:
[tex]\[
23.3 = \frac{57700}{\text{Total Number of Doctors}} \times 100
\][/tex]
3. Rearrange the equation to solve for the total number of doctors:
[tex]\[
\text{Total Number of Doctors} = \frac{57700}{\frac{23.3}{100}}
\][/tex]
4. Simplify the fraction:
First, compute the percentage as a decimal:
[tex]\[
\frac{23.3}{100} = 0.233
\][/tex]
Then, divide the number of female doctors by this decimal:
[tex]\[
\text{Total Number of Doctors} = \frac{57700}{0.233}
\][/tex]
5. Perform the division:
[tex]\[
\frac{57700}{0.233} \approx 247639.14
\][/tex]
6. Round to the nearest whole number:
The total number of registered doctors rounded to the nearest whole number is approximately:
[tex]\[
247639
\][/tex]
Therefore, the total number of registered doctors was approximately 247,639.
