3. The weight is made of an alloy of four metals and weighs 16.3 kg. The weight of the first metal in this alloy is one and a half times greater than that of the second, the weight of the second metal is to the weight of the third as $3: 4$, and the weight of the third to the weight of the fourth - as $5: 6$. Determine the weight of the fourth metal.
Solution. Denoting the weight of the second metal by $x$, express the other weights in terms of $x$. The weight of the first metal will be: $1.5 x$; the weight of the third: $\frac{4}{3} x$; the weight of the fourth: $\frac{24}{15} x$. It is convenient to eliminate the denominators. Then the weights of the metals are respectively: $45 a ; 30 a ; 40 a ; 48 a$. In total, this gives $163 a$ or 16.3 kg. Therefore, $a=0.1$, and the metals weigh 4.5 kg; 3 kg; 4 kg; 4.8 kg.

## Answer: 4.8 kg.

Criteria: 20 points - correct solution (not necessarily the one above); 10 points - the correct equation (or system of equations) was obtained, but errors were made in solving it; $\mathbf{0}$ points - everything else.