4. A problem from the collection LILAVATI, by the Indian mathematician Bhaskara:

For the same price, I bought eight of these rubies, then ten emeralds, and finally a hundred pearls, which you now wear in your earrings. If I add together one of each of these precious stones, their price is only three coins less than half of a hundred.

O wise girl, if you are skilled enough in calculation, just tell me, how many coins did each of these stones cost me then.
4. Denote the price of a ruby as $x$ coins, an emerald as $y$ coins, and a pearl as $z$ coins. The first part of the problem states that $8 x=10 y=100 z$, from which we can express $x=\frac{25}{2} z$ and $y=10 z$. The second part of the problem can be written as the equation $x+y+z=\frac{100}{2}-3$. Therefore, we can write $\frac{25}{2} z+10 z+z=47$ and solve for $z=2$. The pearl costs 2 coins, the emerald 20 coins, and the ruby 25 coins.

Introducing variables: $x$-ruby, $y$-emerald, $z$-pearl .......................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_06886e410b39c0216094g-08.jpg?height=54&width=1639&top_left_y=1572&top_left_x=206)

![](https://cdn.mathpix.com/cropped/2024_06_07_06886e410b39c0216094g-08.jpg?height=54&width=1639&top_left_y=1618&top_left_x=206)

Expressing two variables in terms of the same variable ..............................................................................

Substituting the expressed variables into the equation .......................................................................................................

![](https://cdn.mathpix.com/cropped/2024_06_07_06886e410b39c0216094g-08.jpg?height=57&width=1642&top_left_y=1768&top_left_x=207)