# maths

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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?

• maths -

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;

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