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?
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?
Solution
To solve this problem, we need to break it down into several steps:
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Let's assume the total number of workers in the office is a number that is easily divisible by 3, for example, 90. According to the problem, 1/3 of the workers are women, so there are 30 women and 60 men.
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Half of the women are married, so there are 15 married women. One third of these married women have children, so there are 5 women with children. This means there are 25 women without children.
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Three quarters of the men are married, so there are 45 married men. Two thirds of these married men have children, so there are 30 men with children. This means there are 30 men without children.
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To find the total number of workers without children, we add the number of women without children to the number of men without children. So, 25 women + 30 men = 55 workers without children.
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To find the part of the workers that are without children, we divide the number of workers without children by the total number of workers. So, 55/90 = 0.6111, or approximately 61.11%.
Therefore, approximately 61.11% of the workers are without children.
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