class has 10 more boys than girls 1st day. half the boys leave and there are 10 more girls 2nd day. how many girls are there

Question

a college class has 10 more boys than girls on the first day. on day 2 half the boys leave and there are 10 more girls than boys. how many girls are there in the class?

Answer 1

On the first day, there are X girls and X + 10 boys. 

 

On on the second day, there are half as many boys, or (X + 10)/2. Now there are 10 more girls than boys. So,

 

X = (X + 10)/2 + 10

 

X = 1/2 X + 5 + 10

 

1/2 X = 15

 

So X = 30 girls

 

This checks out. On the first day, there are 30 girls and 40 boys, so there are 10 more boys. On the second day, half the boys leave, so there are 30 girls and 20 boys, or 10 more girls than boys.