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
unit digit of original number ---- x
tens digit of original number ---- x+5
original number = 10(x+5) + x = 11x + 50
number reversed = 10x + (x+5) = 11x + 5
11x+50 + 11x + 5 = 99
22x = 44
x = 2
the original number was 72
check:
72 + 27 = 99 , my answer is correct
To find the original number, let's assign variables to the tens and units digits.
Let's say the tens digit is "T" and the units digit is "U".
We are given that the tens digit is 5 more than the units digit. So, we can write the equation:
T = U + 5
We are also told that when the original number is reversed and added to the original number, the sum is 99.
The original number is composed of the tens and units digits:
Original Number = 10T + U
When this number is reversed, the digits swap places, so it becomes:
Reversed Number = 10U + T
Adding these two numbers gives us the sum:
Original Number + Reversed Number = 99
Substituting the values for the original number and the reversed number:
(10T + U) + (10U + T) = 99
Simplifying this equation:
11T + 11U = 99
Dividing both sides of the equation by 11:
T + U = 9
Now we have a system of equations:
T = U + 5
T + U = 9
We can solve this system by substituting the value of T from the first equation into the second equation:
(U + 5) + U = 9
2U + 5 = 9
2U = 4
U = 2
Now substitute the value of U back into the first equation to find T:
T = 2 + 5
T = 7
Therefore, the original number is 72.