When asked how old she is, a teacher responded with this riddle: “my age is a two digit number. when multiplied by seven, the result is a three digit number. when the digit 6 is written after the three digit number, that number is increased by 1833.” how old is the teacher?

Let x be the age of the teacher.

We know that 7x is a three digit number.

Writing 6 after this number means to multiply this number by 10 (this adds a zero after the number) and then add 6.

So, we actually only need the last information:

Solving this equation is quite trivial: subtract 7x  and 6 from both sides and you get

This is indeed a two digit number, and if you multiply it by 6 it becomes 174, a three digits number.