At first, there were 381 more women than men at the concert hall. By 2 p.m., a total of 276 women and men left the concert hall. There were as many women as men who left the concert hall. In the end, there were 4 times as many women as men who remained behind. How many women were at the concert hall at first?
|
Women |
Men |
Difference |
Before |
4 u + 138 |
1 u + 138 |
381 |
Change |
- 138 |
- 138 |
|
After |
4 u |
1 u |
3 u |
Since there was the same number of men and women that left, the difference between the number of men and women remains unchanged.
3 u = 381
1 u = 381 ÷ 3 = 127
Number of women in the end
= 4 u
= 4 x 127
= 508
Number of women that left
= 276 ÷ 2
= 138
Number of women at first
= 508 + 138
= 646
Answer(s): 646