## 2. At the U supermarket

Jurica is walking through the supermarket and looking around. He likes a book and he also likes a ball. The book is more expensive than the ball by 72 kuna. Jurica notices that for the price of 5 balls, he could buy two such books and still have enough for a chocolate bar. The ball is three times more expensive than the chocolate bar. In the end, Jurica decides to buy one book, one ball, and one chocolate bar. How much will he pay in total?

Result: $\quad 198$
## Solution, first method.

```
Let's denote the price of a chocolate bar by one square.
price of one chocolate:
\square
```

Since a ball is three times
more expensive than a chocolate, the price of a ball can be represented as:

price of one ball:

The book is 72 kuna more expensive than the ball, which can be represented as:

price of one book:

![](https://cdn.mathpix.com/cropped/2024_05_30_033072dbc63a78c728f4g-02.jpg?height=114&width=511&top_left_y=1342&top_left_x=658)

Furthermore, the price of 5 balls is equal to the price of two books and one chocolate.

price of 5 balls:

![](https://cdn.mathpix.com/cropped/2024_05_30_033072dbc63a78c728f4g-02.jpg?height=140&width=1088&top_left_y=1666&top_left_x=678)

price of two books and

1 chocolate

![](https://cdn.mathpix.com/cropped/2024_05_30_033072dbc63a78c728f4g-02.jpg?height=140&width=1085&top_left_x=680&top_left_y=1889)

From the image, it can be concluded that the value of 8 squares, each representing the price of one chocolate, should be $2 \cdot 72=144$.

Therefore, the price of one chocolate is 144 : 8, which is 18 kuna. The price of one ball is $3 \cdot 18$, which is 54 kuna. The price of the book is $54+72$, which is 126 kuna.

For all three items, Jurica paid $126+54+18=198$ kuna at the cash register.

## Solution, second method.

Let's denote the prices of the book, ball, and chocolate by $K, L$, and Č, respectively. We have:

$$
\begin{gathered}
K - L = 72 \\
2K + Č = 5L \\
3Č = L
\end{gathered}
$$

From the second and third equations, we get:

$$
\begin{gathered}
2K + Č = 15Č \\
2K = 14Č \\
K = 7Č
\end{gathered}
$$

Thus, the book costs as much as 7 chocolates. Since the ball is three times more expensive than the chocolate, it follows that the difference in price between the book and the ball ($K - L = 72$) is equal to the price of 4 chocolates:

$$
4Č = 72
$$

From this, we get

$$
Č = 18
$$

Therefore, the price of the chocolate is 18 kuna, the price of the ball is $3 \cdot 18 = 54$ kuna, and the price of the book is

$$
7 \cdot 18 = 126 \text{ kuna.}
$$

For all three items, Jurica paid $126 + 54 + 18 = 198$ kuna at the cash register.