Math Question - Algebra - 27

Question

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

Answer 1

Extra hair means men have beards and women have long hair

x women and y men

Regular hair Extra Hair Totals

Men (2/5)y (3/5)y y

Women (1/3)x (2/3)x x

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Totals 46 (3/5)y + (2/3)x 120

2 equations needed:

x + y = 120

(2/5)y + (1/3)x = 46

(2/5)(y) + (1/3)(120 - y) = 46

6y + 5(120 - y) = 690

6y + 600 - 5y = 690

y + 600 = 690

y = 90

x = 30

90 men and 30 women

(3/5)(90) = 54 have beards ---> 36 do not have beards

(2/3)(30) = 20 have long hair --> 10 do not have long hair

totals are 74 have extra hair and 46 do not (as given)

the table becomes:

Regular hair Extra Hair Totals

Men 36 54 90

Women 10 20 30

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Totals 46 74 120

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