Question

if the unemployment rate is 6 percent and the number of employed is 188 million, then the labor force equals ____ million.
○ 11.28
○ 176.72
○ 188
○ 200

Explanation:

Step1: Recall the unemployment rate formula

The unemployment rate (\(u\)) is given by the formula \(u=\frac{\text{Unemployed}}{\text{Labor Force}}\times100\%\), and the labor force (\(LF\)) is the sum of employed (\(E\)) and unemployed (\(U\)), so \(LF = E+U\). Let the labor force be \(x\) million. Then the number of unemployed is \(x - 188\) million. The unemployment rate is \(6\%=0.06\), so we can write the equation:
\(0.06=\frac{x - 188}{x}\)

Step2: Solve the equation for \(x\)

Multiply both sides of the equation by \(x\):
\(0.06x=x - 188\)

Subtract \(0.06x\) from both sides:
\(0=x- 0.06x-188\)

Simplify the right - hand side:
\(0 = 0.94x-188\)

Add 188 to both sides:
\(0.94x=188\)

Divide both sides by \(0.94\):
\(x=\frac{188}{0.94}=200\)

Answer:

200