B3. The crown of the Syracusan king Hieronymus was made of gold and silver. Its weight in air was $10 \mathrm{kp}$, and under water it was $9 \frac{3}{8} \mathrm{kp}$. Gold loses $\frac{1}{19}$ of its weight under water, and silver loses $\frac{1}{10}$ of its weight under water. How much would the gold and how much the silver in the crown weigh if weighed in air? Write down the answer.
B3. Given that the weight of gold in air was $x \mathrm{kp}$ and that of silver was $y \mathrm{kp}$. Then the following holds: $x+y=10$ and $x-\frac{1}{19} x+y-\frac{1}{10} y=9 \frac{3}{8}$. The solutions to the system are $x=7 \frac{11}{12} \mathrm{kp}$ and $y=2 \frac{1}{12} \mathrm{kp}$. If weighed in air, the gold would weigh $7 \frac{11}{12} \mathrm{kp}$, and the silver would weigh $2 \frac{1}{12} \mathrm{kp}$.

Introduction of variables: $x$ - weight of gold, $y$ - weight of silver ....................................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_4401d59a37898c9fd2b4g-11.jpg?height=51&width=1641&top_left_y=751&top_left_x=276)

![](https://cdn.mathpix.com/cropped/2024_06_07_4401d59a37898c9fd2b4g-11.jpg?height=68&width=1639&top_left_y=794&top_left_x=274)

Correct solving of the system . . ......................................................................................................................

Solutions $x=7 \frac{11}{12} \mathrm{kp}, y=2 \frac{1}{12} \mathrm{kp} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots$

Answer .........................................................................................................