What three-digit number with units digit 2 and hundreds digit 4 is divisible by 9?
To be divisible by 9, a number must have a sum of digits that is a multiple of 9. I can list the possible values of t and their sums: 0 gives 6, 1 gives 7, 2 gives 8, 3 gives 9, 4 gives 10, 5 gives 11, 6 gives 12, 7 gives 13, 8 gives 14, and 9 gives 15. The only one that is a multiple of 9 is 3, so t = 3. Therefore, the three-digit number is 432. 