Math

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3/7 of the people who live in an apartment building are men. 5/8 of the remaining people are women. The rest are children. A total of 220 men and women live in the building. How many people live in the apartment building altogether?

  • Math -

    people in building ---- x (men, women and children)
    children --- y
    men + women + children = x
    (3/7)x + (5/8)(4/7)x + y = x
    3x/7 + 5x/14 + y = x
    times 14
    6x + 5x + 14y = 14x
    14y = 3x

    y + 220 =x
    sub into the other one
    14y = 3(y+220)
    11y = 660
    y = 60
    then 14(60) = 3x ---> x = 280

    So we have 280 people in the building.

    check: 3/7 of 280 are men = 120
    leaving 160 women and children
    5/8 of these ot 100 are women

    so we have 120 men, 100 women and 60 children.

  • Math -

    thanks, there was a similar problem instead of 220 men and women it was 275.. i just substituted

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