the tens digit of a two digit number is 5 more than the units digit. when reversed and added to the original number the answer is 99. find the original number.
To find the original number, we can follow these steps:
Let's start by assuming the original two-digit number is represented as "10x + y", where x is the tens digit and y is the units digit.
According to the given information, we know that the tens digit is 5 more than the units digit. Mathematically, we can represent this as: x = y + 5.
If we reverse the digits and add it to the original number, we get a sum of 99. Reversing the digits of "10x + y" gives us "10y + x". Therefore, the equation is: (10x + y) + (10y + x) = 99.
Now, we can substitute the value of x from the first equation into the second equation. Remember, x = y + 5.
So, (10(y + 5) + y) + (10y + (y + 5)) = 99.
Simplifying this equation, we get: 21y + 15 = 99.
Next, we subtract 15 from both sides of the equation: 21y = 84.
Now, we divide both sides by 21: y = 4.
Using the value of y, we can substitute it back into the equation x = y + 5, which gives us x = 4 + 5 = 9.
Therefore, the original number is 10x + y = 10(9) + 4 = 90 + 4 = 94.
Hence, the original number is 94.