South African Mathematics Olympiad

If I buy $x$ chocolate bars and $y$ cool-drinks, then $25x+9y=839$ with $x>y$. If we put $x=y$ as a first guess, then $x=y=839/34\approx 24$, so we can write $x=24+a$ and $y=24-b$. The equation becomes $25a-9b=23$, which by easy trial and error (guess and check) has a solution $a=2$ and $b=3$. Thus $x=24+2=26$ and $y=24-3=21$, which is the required answer.