Answer:
17
26
35
44
53
62
71
80
Explanation:
Let's solve the problem step by step.
Let's assume the two-digit number is represented as "AB," where A represents the tens digit and B represents the units digit. According to the problem, the difference between the number "AB" and the number "BA" is 54.
So, we have the equation:
(10A + B) - (10B + A) = 54
Simplifying the equation, we get:
9A - 9B = 54
Dividing both sides of the equation by 9, we have:
A - B = 6
Now, we need to find two-digit numbers where the difference between the tens digit and the units digit is 6. The possible combinations are:
(1, 7)
(2, 8)
(3, 9)
(4, 10) - But 10 is not a valid unit digit since it exceeds the range of a two-digit number.
So, the valid two-digit numbers that satisfy the given condition are:
17
26
35
44
53
62
71
80
Therefore, there are 8 two-digit numbers that have a difference of 54 when subtracted from the number formed by reversing their digits.