Final answer:
The student's question is a number puzzle in mathematics where the ones digit must be greater than the tens digit, and their sum with the reverse number is 154. The correct number that satisfies these conditions is 59, since both digits add up to 14 (5 + 9) and the reverse, 95, when summed with 59 equals 154.
Step-by-step explanation:
To solve this problem, let's denote the tens digit as t and the ones digit as o, where the ones digit is taller (or greater) than the tens digit. Since the digits are 0 through 9, t can range from 0 to 8 and o can range from 1 to 9, ensuring that o is greater than t. Given the information that the sum of the number and its reverse is 154, we can write the equation:
10t + o + 10o + t = 154
Simplifying this equation, we combine like terms:
11t + 11o = 154
Dividing both sides by 11 simplifies the equation to:
t + o = 14
Now, since o must be greater than t, we need to find two digits that add up to 14 with one being greater than the other. The pairs that add up to 14 are (5,9), (6,8), and (7,7), but since one digit has to be strictly taller, or larger, than the other, the only suitable pair is (5,9). Thus, the original number is 59 and its reverse is 95. Adding them together, we get:
59 + 95 = 154
So the number we are looking for is 59.