Question 10
There are three fractions, all of which are in lowest terms. The the ratio of their numerators, which are all positive integers, are in the ratio $3:2:4$ while the ratio of their denominators, which are also all positive integers, are in the ratio $5:9:15$. If the sum of these three fractions is $\frac{28}{45}$, what is the sum of their denominators?