5. Karlo bought 5 identical large notebooks and 3 identical small notebooks. If he had bought two more large and two more small notebooks, he would have paid 22 kn more, and if he had bought one more large and three more small notebooks, he would have paid 19 kn more. How much was the bill for the purchased notebooks?

## Tasks worth 10 points:
5. Two large and two small notebooks cost $22 \mathrm{kn}$.
![](https://cdn.mathpix.com/cropped/2024_05_30_7e766adb5f056df76964g-2.jpg?height=338&width=924&top_left_y=708&top_left_x=454)

$=22 \mathrm{kn}$

If the price of a large notebook is denoted by $x$, and the price of a small notebook by $y$, then $2 x+2 y=22$.

Then $x+y=11$ (which can also be concluded from the image, without introducing variables).
![](https://cdn.mathpix.com/cropped/2024_05_30_7e766adb5f056df76964g-2.jpg?height=316&width=416&top_left_y=1144&top_left_x=705)

$=11 \mathrm{kn}$

So, one large and one small notebook together cost 11 kn.

$1 \mathrm{POINT}$

Furthermore, one large and three small notebooks cost 19 kn.
![](https://cdn.mathpix.com/cropped/2024_05_30_7e766adb5f056df76964g-2.jpg?height=328&width=828&top_left_y=1562&top_left_x=498)

$=19 \mathrm{kn}$

Since one large and one small notebook cost 11 kuna, the remaining two small notebooks must be 8 kuna. This can also be concluded as follows:

$(x+y)+y+y=19$

$11+y+y=19$

$2 y=8$

The same can be concluded without variables, from the image:
![](https://cdn.mathpix.com/cropped/2024_05_30_7e766adb5f056df76964g-2.jpg?height=220&width=310&top_left_y=2163&top_left_x=768)

$=8 \mathrm{kn}$

So, two small notebooks cost 8 kn.

2 POINTS

The price of one small notebook is $4 \mathrm{kn}$.

1 POINT

The price of one large notebook is $7 \mathrm{kn}$.

1 POINT

The total bill is $5 \cdot 7+3 \cdot 4=47 \mathrm{kn}$.

1 POINT

TOTAL 6 POINTS

Note: If the student arrived at the solution by guessing, each correct solution should be awarded 1 POINT, plus 1 POINT for the total amount.