a number consists of two digit whose sum is 9 .if 9 is subtracted from the number the digits interchange their places.find the number
54
To find the number, let's break down the problem into steps:
Step 1: Set up the equation based on the given information.
Let's assume the tens digit is represented by 'x' and the units digit is represented by 'y'. According to the problem, the sum of the digits is 9. So we have the equation:
x + y = 9
Step 2: Set up the second equation based on the given information.
If 9 is subtracted from the number, the digits interchange their places. This means the original number minus 9 equals the number formed by swapping the digits. We can represent this as:
10x + y - 9 = 10y + x
Step 3: Solve the equations simultaneously.
Now, we have a system of two equations:
x + y = 9 (Equation 1)
10x + y - 9 = 10y + x (Equation 2)
Simplify Equation 2:
9x - 9 = 9y
Rearrange Equation 1:
x = 9 - y
Substitute x in Equation 2:
9(9 - y) - 9 = 9y
81 - 9y - 9 = 9y
81 - 18 = 18y
63 = 18y
y = 63/18
y = 3.5
Since we are dealing with integers, y can only be a whole number. However, in this case, y is a decimal (3.5), so there is no whole number solution.
Therefore, there is no number that satisfies the given conditions.
a+b=9
10a+b-9 = 10b+a
The number is 54