## SUBJECT II

Given the numbers $a$ and $b, a>b$. If dividing $a$ by their difference results in a quotient of 2 and a remainder of 3, what is the quotient and remainder when $b$ is divided by their difference?

E:14143, nr. 3/2010
## SUBJECT II

Given the numbers $a$ and $b, a>b$. If dividing $a$ by their difference results in a quotient of 2 and a remainder, what is the quotient and remainder when $b$ is divided by their difference?

E:14143, nr. 3/2010

Grading Rubric

Let $\mathrm{d}=\mathrm{a}-\mathrm{b}$, then $\mathrm{a}=2 \mathrm{~d}+3$

2 points

Subtracting $b$ from both sides, we get $a-b=2d-b+3$ $3 points$

or $d=2d-b+3$, from which $b=d+3$. $1 point$

E-mail: isjsalaj@isj.sj.edu.ro

Therefore, the quotient and remainder when $b$ is divided by the difference $a-b$ are 1 and 3, respectively.

1 point