At first, there were 448 more women than men at the concert hall. By 4 p.m., a total of 278 women and men left the concert hall. There were as many women as men who left the concert hall. In the end, there were 3 times as many women as men who remained behind. How many women were at the concert hall at first?
|
Women |
Men |
Difference |
Before |
3 u + 139 |
1 u + 139 |
448 |
Change |
- 139 |
- 139 |
|
After |
3 u |
1 u |
2 u |
Since there was the same number of men and women that left, the difference between the number of men and women remains unchanged.
2 u = 448
1 u = 448 ÷ 2 = 224
Number of women in the end
= 3 u
= 3 x 224
= 672
Number of women that left
= 278 ÷ 2
= 139
Number of women at first
= 672 + 139
= 811
Answer(s): 811