Guess and check.

Calculate for each of these.

12 boys, 0 girl
11 boys, 1 girl
10 boys, 2 girls

And so on, until we get 34 balloons.

You should get 5 boys and 7 girls.

The supposition starts by "supposing" a certain number of people.

You can first start with 12 boys only, or 12 girls only, or even six boys and six girls, whichever you prefer.

You will find that you don't get the correct number of balloons (I assume you know how to multiply and add numbers).

Then, you will change the number of boys and girls and calculate again.

This will take some time to get the answer (unless you are lucky enough to guess it right in the first two tries).