110 of the guests at a concert hall were men. 75% of the remaining guests were women and the rest were children. The number of women was 280 more than the total number of men and children. After some women left the concert hall, 50% of the guests that remained were women. How many women left the concert hall?
Men |
Children |
Women |
Total |
1x4 |
9x4 |
10x4 |
|
1x9 |
3x9 |
|
4 |
9 |
27 |
40 |
|
Men and children |
Women |
Before |
13x1 = 13 u |
27x1 = 27 u |
Change |
|
- 14 u |
After
|
1x13 = 13 u |
1x13 = 13 u |
75% =
75100 =
34 Children : Women = 1 : 3
The total number of children and women at first is repeated. Make the total number of children at first the same. LCM of 9 and 4 is 36.
50% =
50100 =
12 When some women left, the total number of men and children remains unchanged. Make the total number of men and children the same. LCM of 13 and 1 is 13.
The number of women was 280 more than the total number of men and children at first.
Number of more women than the total number of men and children at first
= 27 u - 13 u
= 14 u
14 u = 280
1 u = 280 ÷ 14 = 20
Number of women who left the concert hall
= 27 u - 13 u
= 14 u
= 14 x 20
= 280
Answer(s): 280