## 10. Cash Register

In the cash register of Đurđe, there are banknotes of 100 kuna and 10 kuna, as well as coins of 5 kuna, 2 kuna, and 1 kuna. The total value of the money in the cash register is 1844 kuna. The number of 100 kuna banknotes is one-sixth of the number of 10 kuna banknotes, and the number of 5 kuna coins is half the number of 10 kuna banknotes. The number of 1 kuna coins is one-third of the number of 2 kuna and 5 kuna coins combined, and the number of 2 kuna coins is six more than the number of 5 kuna coins. How many banknotes and coins are there in total in the cash register?

Result: $\quad 158$
## Solution.

Let's denote the number of 100 kuna banknotes as follows:

From the conditions of the problem, we sequentially obtain:

![](https://cdn.mathpix.com/cropped/2024_05_30_adbfbded7af8db94c594g-6.jpg?height=517&width=1453&top_left_y=935&top_left_x=153)

The total value of the money in the cash register can be represented as follows:

| label | value | total |
| :--- | :--- | :--- |
| U-_ and 6 more | 100 | 100 |

Since $183 \bigcirc$ and 14 more kuna amount to 1844 kuna,

then 183

$\bigcirc$ is worth $1844-14=1830 \mathrm{kn}$.

This means that

it is worth $1830: 183=10 \mathrm{kn}$.

In the cash register, there were 10 banknotes of $100 \mathrm{kn}$, 60 banknotes of $10 \mathrm{kn}$, 30 coins of 5 kuna, 36 coins of 2 kuna, and 22 coins of 1 kuna.

In total, there were $10+60+30+36+22=158$ banknotes and coins.