Maths

There were a some men, women , children in a hall.there 1 1/4 times as many men as women,and the ratio of number of women to the number of children is 8:5.when 105 more children entered the hall, the ratio of men to the children changes to 3:2. find the ratio of men to children at first?how many men and women were there in the hall. It gives negative result. Hope may be some mistakes in numbers. Pls guide me

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  1. let the number of women be x
    then the number of men = 1.25x

    women to children = 8:5
    = x : 5x/8

    after 105 children come
    number of children = 5x/8+108

    now :
    1.25x : (5x/8+105) = 3 : 2
    1.25x/(5x/8+105) = 3/2
    15x/8 + 315 = 2.5x
    1.875x + 315 = 2.5x
    x = 504

    So we had 504 women, 630 men and 315 children
    original ratio of men : children = 630:315 = 2 : 1

    check:
    after new kids came, children is 420

    ratio of men : children = 630 : 420 = 3 : 2

    My answers are correct

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