A man want 762 by a number, but he trade it and its quotient result 13 and its rest was 13. What the quotient and rest of the original number? $$ q = ?; r=? $$ $$ 762 = q \cdot \overline{ ab } + r $$ $$ 762 = 13 \cdot \overline {ba} + 21 $$
Another way to write this is: $$ \frac{762-r}{ \overline{ba}}=r $$ $$ \frac{762-21}{ \overline{ba}}=13 $$
You can just solve $762 = 13 \cdot \overline {ba} + 21$ by subtracting $21$ from both sides and dividing by $13$. This gives $\overline {ba}=57$ Then $\overline {ab}=75$ so divide by that.