in a two-digit number the tens-digit is 2 more than the units digit.if the digits are interchanged the sum of the new number and the original number is 88.what is the original number
t = u+2
(10t+u) + (10u+t) = 88
To find the original two-digit number, we can use algebraic equations.
Let's assume the units digit is x.
According to the given information, the tens digit is 2 more than the units digit, which means the tens digit is x + 2.
So, the original number can be written as 10 * (x + 2) + x = 10x + 20 + x = 11x + 20.
When the digits are interchanged, the new number is written as 10x + x + 2 = 11x + 2.
The sum of the new number and the original number is 88, so we can write the equation:
(11x + 2) + (11x + 20) = 88
Simplifying the equation:
22x + 22 = 88
Subtracting 22 from both sides:
22x = 66
Dividing both sides by 22:
x = 3
Now that we know the value of x is 3, we can find the tens digit by substituting it back into the equation for the tens digit:
Tens digit = x + 2 = 3 + 2 = 5
Therefore, the original number is 53.