Two numbers are in the ratio $5 : 7$. If 6 is added to each of them, the ratio becomes $7 : 9$. What is the larger number?

Explanation

1. 01

   Let the numbers be $5k$ and $7k$: $\frac{5k + 6}{7k + 6} = \frac{7}{9}$.

2. 02

   $45k + 54 = 49k + 42$, so $4k = 12$ and $k = 3$.

3. 03

   The numbers are 15 and 21; the larger is 21. Check: $21 : 27 = 7 : 9$.