## Subject (3).

b) To reward students who achieved good results in competitions, a school bought 60 dictionaries of the following types: Romanian Explanatory Dictionary (price 80 RON), English - Romanian / Romanian - English Dictionary (price 31 RON), and Spanish - Romanian / Romanian - Spanish Dictionary (price 30 RON). The total cost for purchasing the dictionaries was 2013 RON. How many dictionaries were bought of each type? Justify your answer! .... 5 points
Solution. $D E X+E / R+S / R=60$ and $80 D E X+31 E / R+30 S / R=2013$. Then $50 D E X+E / R=2013-30 \cdot 60=213$, which clearly forces $E / R \in\{13,63, \ldots\}$; but since we have $E / R \leq 60$, we are left with the possibility $E / R=13$, from which $D E X=4$ and $E / S=43$.