The digit 3 is written at the right of a certain 2-digit number forming a 3-digit number. The new number is 372 more than the original 2-digit number. What is the sum of the digits of the original 2-digit number?
let the 2-digit number be $10a+b$ where $a$ and $b$ are constants. The 3-digit number is produced by the 3 being added which makes it $100a+10b+3$. Then I said $100a+10b+3 = 372+10a+b$. which simplifies to $10a+b = 43$. Therefore the sum of the original 2-digit number is 7. That was not the correct answer when I checked the memorandum.
Where did I go wrong?