How many men and how many women were on the train originally?

Question

The train left Erie with twice as many women as men. At York, 17 men got on and 16 women got off. Now there are as many men as women. How many men and how many women were on the train originally?

Answer 1

Hi Carol,

 

Let n be the original number of men on the train. If there were twice as many women than men, then there were 2n women.

 

At York, 17 men got on and 16 women got off. Now there are n + 17 men and 2n - 16 women. We are told that now there are as many woman as men on the train. So,

 

2n - 16 = n + 17

 

Subtract n from both sides, and add 16 to both sides to get

 

n = 33

 

So, originally, the train had 33 men and 66 women.

 

Check:

Recall that at York, 17 men got on and 16 women got off. So, at that point, the number of men was 33 + 17 = 50, and the number of women was 66 - 16 = 50. So, this is an equal number of men and women.