I am thinking of two two-digit numbers.they differ by 54.Both numbers are made up of the same digits, are reversed.What are the two numbers?
To differ by 54 one must be relatively high and the other low and they need to be even numbers.
Dndndm
To solve this problem, let's break it down step by step.
Step 1: Let's assume the two-digit numbers are XY and YX. Here, X represents the tens digit and Y represents the units digit.
Step 2: We are given that the two numbers differ by 54. So, XY - YX = 54.
Step 3: Since XY is a two-digit number, it is equal to 10X + Y (since the tens digit is multiplied by 10). Similarly, YX is equal to 10Y + X.
Step 4: Substituting the values of XY and YX in the equation XY - YX = 54, we get: (10X + Y) - (10Y + X) = 54.
Step 5: Simplifying the equation, we have: 10X + Y - 10Y - X = 54.
Step 6: Combine like terms: 9X - 9Y = 54.
Step 7: Divide the equation by 9: X - Y = 6.
Step 8: Since the two numbers have the same digits but in reverse order, the difference between the tens digits (X - Y) is 6. The only pair of single-digit numbers that satisfies this condition is (7, 1).
Step 9: So, the two numbers are 71 and 17.
Therefore, the two two-digit numbers that differ by 54 and have the same digits reversed are 71 and 17.