Posted by **Anonymous** on Thursday, February 28, 2013 at 9:54pm.

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 -
**Reiny**, Thursday, February 28, 2013 at 11:03pm
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.

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