7. Which three-digit number increases 26 times when the digit 3 is added to its left?
7. Let $x$ be the sought three-digit number.

Then $\overline{3 x}=26 \cdot x$. 3 POINTS

Further, $3000+x=26 \cdot x$ 2 POINTS

$3000=26 \cdot x-x$ 2 POINTS

$3000=25 \cdot x$ 1 POINT

$x=3000: 25$ 1 POINT

$x=120$.

The sought three-digit number is 120.