If the places of the last two digits of a three digit number are interchanged,a new number greater than the original number by 45 is obtained.what is the difference between the last two digits?
10 u + t = 10 t + u + 45
9 u - 9 t = 45
To solve this problem, let's break it down step by step:
Step 1: Understand the problem.
We are given a three-digit number, and when we interchange the places of the last two digits, we obtain a new number that is 45 greater than the original number. We need to find the difference between the last two digits.
Step 2: Represent the unknowns.
Let's assume the original number is written as "ABC," where A represents the hundreds digit, B represents the tens digit, and C represents the units digit. We want to find the difference between B and C.
Step 3: Express the problem as equations.
According to the problem, if we interchange the places of the last two digits, we obtain a new number greater than the original number by 45. Therefore, we have the equation:
(100A + 10B + C) + 45 = (100A + 10C + B)
Simplifying the equation, we get:
10B + C + 45 = 10C + B
Step 4: Solve the equation.
By rearranging the terms, we can simplify the equation further:
10B - B = 10C - C - 45
9B = 9C - 45
B = C - 5
From this equation, we can conclude that the tens digit (B) is 5 less than the units digit (C).
Step 5: Find the difference between the last two digits.
Since we know that B = C - 5, we can substitute this value into the equation:
B - C = (C - 5) - C
= -5
Therefore, the difference between the last two digits is -5.
In conclusion, the difference between the last two digits is -5.