Fraction. Word problem

Question

There are 280 passengers on board a train. 5/8 of the female passengers and 1/2 of the male passengers are children. There is an equal number of male and female adults. How many children are on board the train?

Answer 1

MALE FEMALE TOTAL

ADULT N N 2N

CHILDREN y x x+y

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TOTALS y+N x+N

x+y+2N = 280

(1/2)(y+N) = y <--- 1/2 of the male passengers are children

(5/8)(x+N) = x <--- 5/8 of the female passengers are children

(1/2)y + (1/2)N = y

(1/2)N = (1/2)y

N=y

(5/8)x + (5/8)N = x

(5/8)N = (3/8)x

5N = 3x

(5/3)N = x

(5/3)N + N + 2N = 280

(4 and 2/3) N = 280

(14/3)N = 280

N = 280*3/14 = 60=y

x=(5/3)(60) = 100

MALE FEMALE TOTALS

ADULT 60 60 120

CHILDREN 60 100 160

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TOTALS 120 160 280

There are 160 children on the train