5. The Metallurgist's Task. The first alloy consists of zinc and copper in a ratio of $1: 2$, while the second alloy contains the same metals in a ratio of $2: 3$. From how many parts of both alloys can a third alloy be obtained, containing the same metals in a ratio of $17: 27$?
5. Let's write the condition of the problem in the form of a table:

| alloys: | weight of zinc (kg) | weight of copper (kg) | take for the new alloy (kg) |
| :---: | :---: | :---: | :---: |
| 1st alloy | $x$ | $2 x$ | $A$ |
| 2nd alloy | $2 y$ | $3 y$ | $B$ |
| new | $x+2 y$ | $2 x+3 y$ |  |

Note that: $\frac{x+2 y}{2 x+3 y}=\frac{17}{27}$, or $27 x+54 y=34 x+51 y$, from which $3 y=7 x$. Since $3 x=A, 5 y=B$, then $\frac{A}{B}=\frac{3 x}{5 y}=\frac{21 x}{35 y}=\frac{9 y}{35 y}=\frac{9}{35}$. The alloys should be taken in the ratio $9: 35$.