Split 57 into two parts so that one-third of the first part is 3 more than one-fifth of the second part. What is the first part?

Explanation

1. 01

   Let the parts be $a$ and $57 - a$: $\frac{a}{3} - \frac{57 - a}{5} = 3$.

2. 02

   Multiply by 15: $5a - 171 + 3a = 45$, so $8a = 216$.

3. 03

   $a = 27$; the second part is 30. Check: $9 - 6 = 3$.