The sum of the digits of a two digit number is 13.The number obtained by interchanging the digits of the given number exceeds that number by 27.Find the number.
Actually, the number is 58.
To find the number, let's start by representing the "tens" and "ones" digits of the two-digit number as variables. Let the tens digit be represented by "x" and the ones digit be represented by "y".
We are given that the sum of the digits is 13, so we can form an equation:
x + y = 13 -- Equation 1
We are also given that the number obtained by interchanging the digits exceeds the original number by 27. This means that the number formed by yx is 27 greater than xy. Mathematically, we can express this as:
10y + x = 10x + y + 27 -- Equation 2
To solve this system of equations, we can first simplify Equation 2:
9y - 9x = 27
Divide both sides of the equation by 9:
y - x = 3 -- Equation 3
Now, we can solve the system of equations by substituting Equation 1 into Equation 3:
x + y = 13
y - x = 3
Adding these two equations, we eliminate the variable "x":
2y = 16
Dividing both sides of the equation by 2:
y = 8
Substituting the value of y back into Equation 1:
x + 8 = 13
Subtracting 8 from both sides:
x = 5
Therefore, the number is 58.