A number has two digits whose sum is 9. If 27 is added to the number,its digits get interchanged. Find the number
the number is AB
A+B=9
10A+B+27=10B+A
A+B=9
9A-9B=-27
can you take if from here?
To find the number, let's assign variables to each of the digits in the number. Let's say the tens digit is "x" and the ones digit is "y".
From the first statement, we know that the sum of the digits is 9, so we can write an equation:
x + y = 9 (equation 1)
Now, let's consider the second statement. If 27 is added to the number, the digits get interchanged. This means the original number can be written as 10y + x (since the tens digit is x and the ones digit is y) and the new number can be written as 10x + y (since the tens digit becomes y and the ones digit becomes x).
So, the equation can be written as:
10y + x + 27 = 10x + y
Simplifying this equation, we get:
9y - 9x = 27 - 27
9y - 9x = 0 (equation 2)
Now, we have a system of two equations (equation 1 and equation 2) with two variables (x and y). We can solve these equations to find the values of x and y, and consequently, the number.
To solve this system of equations, let's use the method of substitution:
From equation 2, we can express y in terms of x:
y = x
Now, substitute y = x in equation 1:
x + x = 9
2x = 9
x = 9/2
Since x has to be a whole number, x = 4.
Substitute the value of x back into equation 1:
4 + y = 9
y = 9 - 4
y = 5
Therefore, the number is 45.