The average height of 3 men is 175 cm. the average height of 2 women is 160 cm. find the average height of the 5 people.

Hi Xin,
Please find below the solution to the asked query :

$$\begin{gathered} \mathrm{We} \mathrm{have}, \\ \mathrm{average} \mathrm{height} \mathrm{of} 3 \mathrm{men} = 175 \mathrm{cm} \\ \Rightarrow \frac{\mathrm{sum} \mathrm{of} \mathrm{heights} \mathrm{of} 3 \mathrm{men}}{3} = 175 \\ \Rightarrow \mathrm{sum} \mathrm{of} \mathrm{heights} \mathrm{of} 3 \mathrm{men} = 525 \mathrm{cm} \\ \mathrm{average} \mathrm{height} \mathrm{of} 2 \mathrm{women} = 160 \mathrm{cm} \\ \Rightarrow \frac{\mathrm{sum} \mathrm{of} \mathrm{heights} \mathrm{of} 2 \mathrm{women}}{2} = 160 \\ \Rightarrow \mathrm{sum} \mathrm{of} \mathrm{heights} \mathrm{of} 2 \mathrm{women} = 320 \mathrm{cm} \\ \mathrm{Now}, \mathrm{sum} \mathrm{of} \mathrm{the} \mathrm{heights} \mathrm{of} 5 \mathrm{people} = \mathrm{sum} \mathrm{of} \mathrm{heights} \mathrm{of} 3 \mathrm{men} + \mathrm{sum} \mathrm{of} \mathrm{heights} \mathrm{of} 2 \mathrm{women} \\ \Rightarrow \mathrm{sum} \mathrm{of} \mathrm{the} \mathrm{heights} \mathrm{of} 5 \mathrm{people} = 525 + 320 = 845 \mathrm{cm} \\ \mathrm{average} \mathrm{height} \mathrm{of} 5 \mathrm{people} = \frac{\mathrm{sum} \mathrm{of} \mathrm{the} \mathrm{heights} \mathrm{of} 5 \mathrm{people} }{5} \\ \Rightarrow \mathrm{average} \mathrm{height} \mathrm{of} 5 \mathrm{people} = \frac{845}{5} = 169 \mathrm{cm} \end{gathered}$$

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