Let's represent the number of purple balloons as P. We know that there are 2 green balloons for every 3 purple balloons, which can be represented as:
G = 2P/3
We also know that there are 10 balloons in total for each arrangement. Combining these two pieces of information, we get:
10 = P + 2P/3
Solving for P, we get:
10 = P + 2P/3
3P = 90
P = 30
So, there are 30 purple balloons in the balloon arrangement.