Sophie wrote a two-digit number on the board. Max wrote the digit 3 to the right of it and got a number that is bigger than the Sophie's number by 372. What number did Sophie write on the board?

41

Step-by-step explanation:

Let the number written by Sophie be xy. Now Max wrote 3, the number now looks like xy3.

From the question, we know that:

xy3 - xy = 372

We can see from here obviously that 3 - y = 2

This makes y equals to 1

Now we have x13 - x1 = 372

In the first x13, x stands for hundreds, 1 stands for tens and 3 as units. In the second s stands for tens and 1 as units. This essentially mean:

(100x + 10 + 3) - (10x + 1) = 372

100x + 10 + 3 - 10x - 1 = 372

90x + 12 = 372

90x = 372 - 12

90x = 360

x = 360/90 = 4