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