There ere 258 pupils in the hall.If 1/3 of the boys left the hall and 22 girls entered the hall, there would be an equal number of boys and girls in the hall.

1) How many boys were in the hall at first?
2)Ho many more boys than girls were in the hall at first?

You can set the number of boys to be x and the number of girls to be y.

After a third of the boys leave, you are left with 2/3x. 22 new girls arrive, so you get y+22

Now, you have a system of equations:
x+y = 256
2x/3 = y+22

Express y in terms of x in second equation:
y= 2x/3 -22

Set 2x/3 -22 into the first equation in stead of y.

(2x/3)-22+x = 258
5x/3 = 280
x=168

That means that y = 258-168 = 90

Controll: 90+22=112; 168*2/3=112;

To find the number of boys in the hall at first, we can start by assuming that the number of boys is x. We'll go step by step to solve the problem.

1) Let's solve for the equation when there are an equal number of boys and girls in the hall after 1/3 of the boys leave and 22 girls enter the hall.

Given:
Total pupils in the hall = 258

After 1/3 of the boys leave, the number of boys left = x - (1/3)x = (2/3)x
After 22 girls enter, the number of girls = 22

According to the problem, the number of boys and girls will be equal: (2/3)x = 22

To find the value of x, we can cross multiply:

2x = 22 * 3
2x = 66
x = 33

Therefore, there were 33 boys in the hall at first.

2) To find the difference between the number of boys and girls in the hall at first, we can subtract the number of girls from the number of boys:

Difference = Number of boys - Number of girls
= x - 22
= 33 - 22
= 11

Therefore, there were 11 more boys than girls in the hall at first.