A 2-digit number is one more than 6 times the sum of its digits. If the digits are reversed, the new number is 9 less than the original number.

Question

How to teach kids to solve this problem?

A 2-digit number is one more than 6 times the sum of its digits. If the digits are reversed, the new number is 9 less than the original number. Find the original number.

Answer 1

$$10 a + b - 1 = 6 (a + b)$$

$$10 b + a + 9 = 10 a + b$$

Solve those.

Answer 2

If the kids are too young to be familiar with solving linear equations, one can motivate them to look for pattern.

Adding $9$ to a two-digit number reduces its units digit by $1$. This new units digit was tens digit of original. The required number is of the form $$\overline{(d-1)d}$$

where $d \in \{1,2,\ldots, 9\}$. There is only a few of them and one of them satisfies the other condition.