The difference between a two-digit number and that number reversed is 18. What could the numbers be?
24 and 42
35 and 53
and so on, where the digits differ by 2
13, 31
24, 42
35, 53
46, 64
57, 75
68, 86
79, 97
To find the two-digit numbers that satisfy the given condition, we can approach this problem systematically:
Step 1: Let's assume the two-digit number is represented as "10a + b" (where a is the tens digit and b is the units digit).
Step 2: The reversed number can be represented as "10b + a".
Step 3: According to the given condition, the difference between the original number and its reversed form is 18. Therefore, we can set up the equation:
(10a + b) - (10b + a) = 18
Step 4: Simplifying the equation:
10a + b - 10b - a = 18
9a - 9b = 18
a - b = 2
Step 5: From the equation a - b = 2, we can try different combinations of values for a and b in order to find the two-digit numbers that satisfy the equation.
By considering different values, we can find the following potential solutions:
a = 3, b = 1 ===> 31 - 13 = 18
a = 4, b = 2 ===> 42 - 24 = 18
a = 5, b = 3 ===> 53 - 35 = 18
a = 6, b = 4 ===> 64 - 46 = 18
a = 7, b = 5 ===> 75 - 57 = 18
a = 8, b = 6 ===> 86 - 68 = 18
a = 9, b = 7 ===> 97 - 79 = 18
Therefore, the two-digit numbers that satisfy the given condition are: 31, 42, 53, 64, 75, 86, and 97.