In response to the poster’s comments on preference not to use algebra, i have devised a different approach using the model drawing. It is slightly complicated and not sure if you can follow my train of thought.
Refer to my above model drawing.
35% of the new balloons are yellow which means
65% of the new balloons are blue
So far so good. OK. Here comes the tricky part.
We know that in the end, the blue balloons have 3 units more than the yellow balloons.
And we know that out of the additional balloons added, there is 30% more blue balloons (65%-35%)
Hence that 30% of new balloons is represented by the extra 3 units in our model drawing!
This means that every 10% of new balloons is represented by 1 unit in our drawing
Therefore the extra new yellow balloons (35%) is actually 3.5 units and the extra new blue balloons (65%) is actually 6.5 units
Since Yellow balloons has 5 units, this means that our original 60 yellow balloons is represented by 1.5 units (5 – 3.5).
Hence, 1 unit = 60/1.5 = 40
13 units = 40 x 13 = 520 balloons!
Would this approach be better?