At first, there were 414 more women than men at the museum. By 3 p.m., a total of 270 women and men left the museum. There were as many women as men who left the museum. In the end, there were 3 times as many women as men who remained behind. How many women were at the museum at first?
|
Women |
Men |
Difference |
Before |
3 u + 135 |
1 u + 135 |
414 |
Change |
- 135 |
- 135 |
|
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 = 414
1 u = 414 ÷ 2 = 207
Number of women in the end
= 3 u
= 3 x 207
= 621
Number of women that left
= 270 ÷ 2
= 135
Number of women at first
= 621 + 135
= 756
Answer(s): 756