The show

At a show, two-fifths of the people are men, and the rest are women. 30% of the men are over 60 years old. 40% of the women are over 60 years old. What fraction of the people are less than 60 years?

Correct answer:

x =  16/25

Step-by-step explanation:

$$\begin{gathered} m=\frac{2}{5}=0.4 \\ w=1-m=1-\frac{2}{5}=\frac{1\cdot 5}{5}-\frac{2}{5}=\frac{5}{5}-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}=0.6 \\ {r}_1=30\%=\frac{30}{100}=\frac{3}{10}=0.3 \\ {r}_2=40\%=\frac{40}{100}=\frac{2}{5}=0.4 \\ {r}_3=1-r_1=1-\frac{3}{10}=\frac{1\cdot 10}{10}-\frac{3}{10}=\frac{10}{10}-\frac{3}{10}=\frac{10-3}{10}=\frac{7}{10}=0.7 \\ {r}_4=1-r_2=1-\frac{2}{5}=\frac{1\cdot 5}{5}-\frac{2}{5}=\frac{5}{5}-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}=0.6 \\ {x}_1=m\cdot r_3=\frac{2}{5}\cdot \frac{7}{10}=\frac{2\cdot 7}{5\cdot 10}=\frac{14}{50}=\frac{7}{25}=0.28 \\ {x}_2=w\cdot r_4=\frac{3}{5}\cdot \frac{3}{5}=\frac{3\cdot 3}{5\cdot 5}=\frac{9}{25}=0.36 \\ x=x_1+x_2=\frac{7}{25}+\frac{9}{25}=\frac{7+9}{25}=\frac{16}{25}=0.64 \end{gathered}$$

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