Three-fifths of the men in chemistry class have beards and two-thirds of the women have long hair. If there are 120 men in the class and 46 are not in the above groups, how many men and how many women are there in the class?

Question

Colton Christensen

Mathematics

12 December, 01:40

Three-fifths of the men in chemistry class have beards and two-thirds of the women have long hair. If there are 120 men in the class and 46 are not in the above groups, how many men and how many women are there in the class?

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Answers (1)

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Weston Juarez · Answer 1

The question doesn't tell the amount of the women so I think the "120 men" mean that there are "120 people" (men+women) in the class.

That mean 46 people which are not "above group" consist of 2/5 men (without beards) and 1/3 women (without long hair).

You can get this equation:

46 = 2/5men + 1/3women

74 = 3/5men + 2/3women

120 = men + women

You can change the first equation into this

46 = 2/5men + 1/3women

1/3women = 46 - 2/5 men

women = 138 - 6/5 men

Add the first equation into the second

74 = 3/5men + 2/3women

74 = 3/5men + 2/3 (138 - 6/5 men)

74 = 3/5men + 92 - 4/5men

74 = - 1/5 men + 92

1/5 men = 92-74

men = 18 * 5 = 90

Using the 3rd equation

120 = men + women

women = 120-90 = 30

The answer would be: 90 men, 30 women