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In a certain office, 1/3 of workers are women, 1/2 of the women are married and 1/3 of the married women have children. If 3/4 of the men are married and 2/3 of the married men have children, what part of the workers are without children?Options 4/95/1811/1817/36

Question

In a certain office, 1/3 of workers are women, 1/2 of the women are married and 1/3 of the married women have children. If 3/4 of the men are married and 2/3 of the married men have children, what part of the workers are without children?Options 4/95/1811/1817/36

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Solution

Let's break down the problem step by step.

  1. Let the total number of workers be W W .

  2. The number of women workers is 13W \frac{1}{3}W .

  3. The number of married women is 12×13W=16W \frac{1}{2} \times \frac{1}{3}W = \frac{1}{6}W .

  4. The number of married women with children is 13×16W=118W \frac{1}{3} \times \frac{1}{6}W = \frac{1}{18}W .

  5. The number of women without children is 13W118W=618W118W=518W \frac{1}{3}W - \frac{1}{18}W = \frac{6}{18}W - \frac{1}{18}W = \frac{5}{18}W .

  6. The number of men workers is W13W=23W W - \frac{1}{3}W = \frac{2}{3}W .

  7. The number of married men is 34×23W=12W \frac{3}{4} \times \frac{2}{3}W = \frac{1}{2}W .

  8. The number of married men with children is 23×12W=13W \frac{2}{3} \times \frac{1}{2}W = \frac{1}{3}W .

  9. The number of men without children is 23W13W=13W \frac{2}{3}W - \frac{1}{3}W = \frac{1}{3}W .

  10. The total number of workers without children is 518W+13W \frac{5}{18}W + \frac{1}{3}W .

  11. Convert 13W \frac{1}{3}W to a common denominator of 18: 13W=618W \frac{1}{3}W = \frac{6}{18}W .

  12. Add the fractions: 518W+618W=1118W \frac{5}{18}W + \frac{6}{18}W = \frac{11}{18}W .

Therefore, the part of the workers without children is 1118 \frac{11}{18} .

This problem has been solved

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