## SUBJECT 3

The quotient of the division of two natural numbers is 3, and the remainder is 7. If we triple the dividend, then the remainder is 6. Determine the numbers.

RMT 2/2009
## SUBJECT 3

The quotient of the division of two natural numbers is 3, and the remainder is 7. If we triple the dividend, then the remainder is 6. Determine the numbers.

| Let a and b be the two numbers. Then $a=3b+7$, with $b>7$. | $2 p$ |
| :--- | :--- |
| Multiplying the previous equality by 3, we have $3a=9b+21$, or $3a=(9b+15)+6$. | $1 p$ |
| $(9b+15)$ is exactly divisible by b, | $1 p$ |
| $9b$ is exactly divisible by b, so 15 is exactly divisible by b. | $1 p$ |
| But $b>7$, so b $=15$. | $1 p$ |
| And then $a=3 \cdot 15+7=52$. | $1 p$ |