Paul is 14 and Luis is 21.
We can use the proportion as the coefficients of a variable, x, to help us solve this.
2x+3x=35 (because the ratio of their ages is 2:3, and the sum of their ages is 35)
5x=35
Divide both sides by 5:
5x/5 = 35/5
x = 7
This means that Paul's age is 2*7=14 and Luis's age is 3*7=21.