4. In an urn, there are white, red, and green balls. Knowing that the number of white balls is 35 more than the red ones, the number of red balls is three times less than the green ones, and the number of green balls is 19 more than the white ones, determine how many balls of each color are in the urn.

(7 points)

$E: 14379$ from GM 3/2013

NOTE: All subjects are mandatory.

Each subject is graded from 0 to 7 points.

Working time 2 hours.

Each subject should be written on a separate sheet.

## National Mathematics Olympiad - local stage - February 16, 2014  5th Grade

Variant 2

## GRADING and SCORING GUIDE:
## 4. SOLUTION

Let a be the number of white balls, r be the number of red balls, and v be the number of green balls.
$\mathrm{a}=\mathrm{r}+35$
...... 1 p
$\mathrm{v}=3 \mathrm{r}$
$v=a+19 \Rightarrow v=r+35+19=r+54$
$3 r=54 \Rightarrow r=27 ; a=62 ; v=81$

Finalization