Hi Audrey,

You can certainly use algebra to solve this problem.

Suppose the digits are m and n so the number is 10m + n. You know two facts

The sum of the digits is 9

m + n = 9

If the digits are reversed, the new number if 63 greater than the original number.

10n + m = 10m + n + 63

Solve these two equations for m and n.

There is however an easier and more insightful way to solve the problem. It involves knowing one fact.

If the sum of the digits of a number s divisible by 9 then the number is divisible by 9.

The sum of the digits of the two-digit number you started with is 9 which is divisible by 9. Hence the two-digit number is divisible by 9. What are the two-digit numbers which are divisible by 9?

2 × 9 = 18
3 × 9 = 27
4 × 9 = 36
.
.
.
11 × 9 = 99

Add 63 to each of these. Which one results in a two-digit number with the digits reversed?

Penny