Task 1. Given the fraction $\frac{57}{71}$. What number needs to be subtracted from the numerator and the same number added to the denominator so that the value of the fraction after simplification is $\frac{1}{3}$?
Solution. The following equation needs to be solved: $\frac{57-x}{71+x}=\frac{1}{3}$. Therefore: $3(57-x)=71+x$, i.e., $171-3 x=71+x, 171-71=x+3 x, 100=4 x, x=25$.