4. The sum of three natural numbers is 3053. If we divide the first number by half of the second, we get a quotient of 3 and a remainder of 5, and if we divide the third number by a quarter of the second, we get a quotient of 5 and a remainder of 3.

Find the numbers.
Solution:

Let the second number be $4 x$. . . . 1p

The first number will be $3 \cdot 2 x+5=6 x+5$. . . $1 p$

The third number will be $5 x+3$. . . . 1 p

We obtain the equation: $15 x+8=3053$, with the solution $x=203$. $1 p$

Finalization:

The first number will be $6 \cdot 203+5=1223$. . . . 1p

The second number will be $4 \cdot 203=812$. . . . 1 p

The third number will be $5 \cdot 203+3=1018$

$1 p$

## Total: $7 p$