At first, there were 416 more women than men at the concert hall. By 4 p.m., a total of 266 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 + 133 |
1 u + 133 |
416 |
Change |
- 133 |
- 133 |
|
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 = 416
1 u = 416 ÷ 2 = 208
Number of women in the end
= 3 u
= 3 x 208
= 624
Number of women that left
= 266 ÷ 2
= 133
Number of women at first
= 624 + 133
= 757
Answer(s): 757