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In a recent year, $26.6\%$ of all registered doctors were female. If there were $58,600$ female registered doctors that year, what was the total number of registered doctors? $\newline$ Round your answer to the nearest whole number.

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Exponential growth and decay: word problems

Full solution

Q. In a recent year,

26.6\%

of all registered doctors were female. If there were

58,600

female registered doctors that year, what was the total number of registered doctors?

\newline

Round your answer to the nearest whole number.

Understand percentage and number: Understand the percentage and the actual number given. $\newline$ We know that $26.6\%$ of the total number of registered doctors were female, and there were $58,600$ female registered doctors.
Convert percentage to decimal: Convert the percentage to a decimal to use in calculations. $\newline$ To convert a percentage to a decimal, divide by $100$ . $\newline$ $26.6\% = \frac{26.6}{100} = 0.266$
Set up equation for total: Set up the equation to find the total number of registered doctors. Let the total number of registered doctors be $T$ . The number of female doctors is $26.6\%$ of the total, which is $0.266 \times T$ . We know the number of female doctors is $58,600$ . So, $0.266 \times T = 58,600$ .
Solve for total: Solve for $T$ , the total number of registered doctors. Divide both sides of the equation by $0.266$ to isolate $T$ . $T = \frac{58,600}{0.266}$
Calculate total: Calculate the total number of registered doctors. $\newline$ $T = \frac{58,600}{0.266}$ $\newline$ $T \approx 220,300.75$
Round to nearest whole number: Round the answer to the nearest whole number. $\newline$ Since we cannot have a fraction of a doctor, we round to the nearest whole number. $\newline$ $T \approx 220,301$

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