Posted by Anonymous on .
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,
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 
Edward,
thanks, there was a similar problem instead of 220 men and women it was 275.. i just substituted