## 1. task

On a shelf in a bookstore, there are six mathematics books whose prices are $62 \mathrm{kn}, 63 \mathrm{kn}, 66 \mathrm{kn}, 68 \mathrm{kn}, 69 \mathrm{kn}$, and 71 kn. Both Jure and Duje bought books from this shelf, and Duje spent four times as much as Jure, with only one book remaining on the shelf. Which books did each of them buy and how much did they pay for them? What is the price of the unsold book?
## Solution:

All the books together cost $399 \mathrm{kn}$.

Duje spent four times more than Jure, so together they paid five times more than what Jure paid for his books. This means that the total cost of the purchased books is a multiple of the number 5, which is only true if the unsold remaining book is worth $69 \mathrm{kn}$.

Jure and Duje together paid $399-69=330 \mathrm{kn}$. Jure paid $330: 5=66 \mathrm{kn}$, and Duje $264 \mathrm{kn}$.

Duje bought books worth 62, 63, 68, and 71 kn, and Jure bought a book worth 66 kn.