The ratio of the number of men to the number of women in a 20 member committee is 3:1. How many women must be added to the 20-member committee so as to make the ratio of men to women 3:2?
20 members in the ratio 3:1
Number of women = \(\frac{1}{4} \times 20\)
= 5
Let the number of women to be added = x
Total number of members in the committee = 20 + x
\(\frac{5 + x}{20 + x} = \frac{2}{5}\)
\(5(5 + x) = 2(20 + x)\)
\(25 + 5x = 40 + 2x \implies 5x - 2x = 40 - 25\)
\(3x = 15 \implies x = 5\)
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