4. Let $A=$ the set of red balls, $B=$ the set of yellow balls, $C=$ the set of green balls, where $A, B, C$ are pairwise disjoint.

We have: $\operatorname{card} A+\operatorname{cardB}=17, \operatorname{cardB}+\operatorname{card} C=29$ (2p)

Subtract the first relation from the second and obtain cardC - cardA $=12$. .(1p)

But $\operatorname{cardC}=2 \cdot \operatorname{card} A \Rightarrow \operatorname{card} A=12, \operatorname{cardB}=5, \operatorname{card} C=24$ (3p)

## MATHEMATICS OLYMPIAD  LOCAL PHASE, 09.02.2013  5th Grade
4. (7p) In a box, there are red, yellow, and green balls. Only 17 of them are not green and only 29 are not red. The red ones are half as many as the green ones. Determine the number of balls of each color.

Liviu Cocariu-Ardelean

Note: All questions are mandatory.

Actual working time: 2 hours.