3. $(5-7,8)$ Nезнayka and Ponchik have the same amounts of money, composed of coins worth $1, 3, 5$, and 7 ferthings.

Nезнayka has as many 1-ferthing coins as Ponchik has 3-ferthing coins;

3-ferthing coins - as many as Ponchik has 5-ferthing coins; 5-ferthing coins - as many as Ponchik has 7-ferthing coins; and 7-ferthing coins - as many as Ponchik has 1-ferthing coins;

Determine how many 7-ferthing coins Nезнayka has, given that each has 20 coins.
Answer: 5 coins.

Solution: Let $x, y, z, t$ be the number of 1, 3, 5, and 7-ferting coins that Nезнайка has. It is known that $x+y+z+t=20$ and $x+$ $3 y+5 z+7 t=3 x+5 y+7 z+t$. From the last equation, it follows that $6 t=2(x+y+z)$. Substituting $x+y+z=20-t$, we get the equation $6 t=2(20-t)$, the solution of which is $t=5$.