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In the department, 3/5 of the workers are men and the rest are women.
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20 Dec 2022, 07:54
20 Dec 2022, 07:54
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Question Stats:
93% (01:45) correct
6% (02:08) wrong based on 15 sessions
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In the department, 3/5 of the workers are men and the rest are women. If 1/2 of the men and 3/7 of the women in the department are over 35, what fraction of all the workers in the department are over 35?
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33/70
Re: In the department, 3/5 of the workers are men and the rest are women.
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30 Jan 2023, 03:15
30 Jan 2023, 03:15
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3/5 of the workers are men, and of those, 1/2 over 35.
3/5*1/2=3/10 of the workers are men over 33. Similarly,
(1-3/5)*3/7=6/35 of the workers are women over 35. The total fraction of workers over 35, noting that the least common denominator of io and 35 is 70, is given by:
3/10+6/35=33/70
3/5*1/2=3/10 of the workers are men over 33. Similarly,
(1-3/5)*3/7=6/35 of the workers are women over 35. The total fraction of workers over 35, noting that the least common denominator of io and 35 is 70, is given by:
3/10+6/35=33/70
In the department, 3/5 of the workers are men and the rest are women.
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24 Jan 2024, 02:20
24 Jan 2024, 02:20
1
The fraction of men \(= \frac{3}{5}\)
The fraction of women \(= \frac{2}{5}\)
The fraction of men over 35 \(= \frac{1}{2} \times \frac{3}{5} = \frac{3}{10}\)
The fraction of women over 35 \(= \frac{3}{7} \times \frac{2}{5 }= \frac{6}{35}\)
Total fraction of men and women over 35 is \(\frac{3}{10} + \frac{6}{35} = \frac{3 \times 7 + 6 \times 2}{70}= \frac{21 + 12}{70} = \frac{33}{70}\)
The answer is \(\frac{33}{70}\)
The fraction of women \(= \frac{2}{5}\)
The fraction of men over 35 \(= \frac{1}{2} \times \frac{3}{5} = \frac{3}{10}\)
The fraction of women over 35 \(= \frac{3}{7} \times \frac{2}{5 }= \frac{6}{35}\)
Total fraction of men and women over 35 is \(\frac{3}{10} + \frac{6}{35} = \frac{3 \times 7 + 6 \times 2}{70}= \frac{21 + 12}{70} = \frac{33}{70}\)
The answer is \(\frac{33}{70}\)
