At a presidential debate, 60% of the participants were men and the rest were women. When 140 more participants arrived, the number of men increased by 20% and the number of women increased by 40%. How many participants were at the debate?

Answer 1

Let the number of participants at the debate be x.

Initially, 60% of the participants were men, so the number of men = 0.6x
The remaining participants were women, so the number of women = 0.4x

After 140 more participants arrived, the number of men increased by 20%, so the new number of men = 0.6x + 0.2*(0.6x) = 0.72x
The number of women also increased by 40%, so the new number of women = 0.4x + 0.4*(0.4x) = 0.56x

Total number of participants after the increase = x + 140
Total number of men after the increase = 0.72x
Total number of women after the increase = 0.56x

According to the given information:
0.72x + 0.56x = x + 140
1.28x = x + 140
0.28x = 140
x = 140 / 0.28
x = 500

Therefore, there were initially 500 participants at the debate.