sum of the digits of a two digit number is 12. the given number exceeds the number obtained by interchanging the digit by 36. find the given number.
If the number is xy, then
x+y=12
10x+y = 36+10y+x
Now just find x and y.
If that's too hard, just think of the pairs of digits that add to 12, and try them out.
To find the given number, let's assume the tens digit of the number is x and the units digit is y.
Given:
1. The sum of the digits of a two-digit number is 12.
So, we have the equation: x + y = 12.
2. The given number exceeds the number obtained by interchanging the digits by 36.
This gives us the equation: 10x + y = 10y + x + 36.
Now, let's solve these equations to find the values of x and y, and hence the given number.
From equation 1:
x + y = 12
Multiplying equation 1 by 10 gives us:
10x + 10y = 120
Subtracting x + y from the above equation gives us:
10x + 10y - x - y = 120 - 12
9x + 9y = 108
Dividing both sides of the equation by 9 gives us:
x + y = 12
Simplifying further, we get:
x + y = 12
9x + 9y = 108
Now, let's solve these equations simultaneously.
Subtracting x + y from 9x + 9y, we have:
9x + 9y - (x + y) = 108 - 12
8x + 8y = 96
Dividing both sides of the equation by 8 gives us:
x + y = 12
Simplifying further, we get:
x + y = 12
x + y = 12
Since both equations are the same, we can conclude that there are infinite solutions. Therefore, the given number could be any two-digit number where the sum of the digits is 12.
For example, the given number could be 39, 93, 84, 48, etc.