Answer:
Let's call the three digits of the three-digit number "a", "b", and "c". Since the product of the digits is 135, we know that:
a * b * c = 135
We need to find the value of a + b + c. One way to approach this is to try out different combinations of digits that multiply to 135 and see which one adds up to the correct sum. The possible combinations are:
1 * 3 * 45 = 135 -> 1 + 3 + 45 = 49
1 * 5 * 27 = 135 -> 1 + 5 + 27 = 33
1 * 9 * 15 = 135 -> 1 + 9 + 15 = 25
3 * 5 * 9 = 135 -> 3 + 5 + 9 = 17
So, the only combination of digits that adds up to a three-digit number is 1, 3, and 45, which add up to 49. Therefore, the answer is 49.