Problem 4. Ivan thought of a number. The number he thought of is three times smaller than the arithmetic mean of five consecutive even numbers. $75\%$ of the value of the first number in the sequence of consecutive even numbers is equal to the arithmetic mean of the first number in the sequence and the number Ivan thought of. What number did Ivan think of?
Solution. Let $x$ be the number Ivan thought of and let the sequence of five consecutive even numbers be $y, y+2, y+4, y+6, y+8$, where $y$ is an even number. Then, from the conditions, we get the system $3 x=\frac{y+(y+2)+(y+4)+(y+6)+(y+8)}{5}$, $\frac{75}{100} y=\frac{y+x}{2}$, from which by simplification we obtain $3 x=y+4, 3 y=2 y+2 x$, or $x=4, y=8$. Therefore, Ivan thought of the number 4.