2. (7p) Three children buy markers, notebooks, and pencils, each type of object being the same, and pay as follows:

- the first, for 12 markers, 8 notebooks, 8 pencils, 60 lei;
- the second, for 4 markers, 8 notebooks, 2 pencils, 30 lei;
- the third, for 8 markers, 4 notebooks, and 6 pencils, 38 lei.

Determine the price of each of the three types of objects bought.

Liviu Cocariu-Ardelean
2. Comparative method: presenting the data in the form of the following scheme ................... (2p)

First child ....... 12 markers ...... 8 notebooks ...... 8 pencils ...... 60 lei

Second child ..... 4 markers ...... 8 notebooks ...... 2 pencils ...... 30 lei

Third child ..... 8 markers ...... 4 notebooks ...... 6 pencils ...... 38 lei

Adding the items purchased by the last two children we get:

12 markers ...... 12 notebooks ...... 8 pencils ...... 68 lei ..................................1p)

$\Rightarrow 4$ notebooks cost 8 lei $\Rightarrow 1$ notebook costs 2 lei .......................................................................1p)

We have 12 markers ...... 8 pencils ...... $60-8 \cdot 2=44$ lei

4 markers ...... 2 pencils ...... $30-8 \cdot 2$ = 14 lei $\mid \cdot 4$..........................................1p)

$\Rightarrow \quad 16$ markers ...... 8 pencils ...... 56 lei $\Rightarrow 4$ markers cost $56-44=12$ lei

$\Rightarrow 1$ marker costs 3 lei

$\Rightarrow 1$ pencil costs 1 lei