To determine the unemployment rate in the given scenario, follow these steps:
1. Calculate the labor force:
The labor force is the total working-age population minus the people not in the labor force.
[tex]\[
\text{Labor Force} = \text{Total Working-Age Population} - \text{Not in Labor Force}
\][/tex]
Given:
- Total working-age population = 120 million
- Not in labor force = 50 million
[tex]\[
\text{Labor Force} = 120\,\text{million} - 50\,\text{million} = 70\,\text{million}
\][/tex]
2. Calculate the number of unemployed people:
The number of unemployed people is the labor force minus the number of employed people.
[tex]\[
\text{Unemployed People} = \text{Labor Force} - \text{Employed People}
\][/tex]
Given:
- Employed people = 66.5 million
[tex]\[
\text{Unemployed People} = 70\,\text{million} - 66.5\,\text{million} = 3.5\,\text{million}
\][/tex]
3. Calculate the unemployment rate:
The unemployment rate is calculated by dividing the number of unemployed people by the labor force and then multiplying by 100 to convert it to a percentage.
[tex]\[
\text{Unemployment Rate} = \left( \frac{\text{Unemployed People}}{\text{Labor Force}} \right) \times 100
\][/tex]
[tex]\[
\text{Unemployment Rate} = \left( \frac{3.5\,\text{million}}{70\,\text{million}} \right) \times 100
\][/tex]
Simplifying the fraction:
[tex]\[
\text{Unemployment Rate} = \left( \frac{3.5}{70} \right) \times 100 = 0.05 \times 100 = 5
\][/tex]
Therefore, the unemployment rate is [tex]\( 5 \)[/tex].
