The sum of the digits of a two-digit number is 14. The number formed by reversing the digits is 36 more than the original number. What is the original number?
let the 10 digit number be x
let the one digit number be y
x + y = 14 , y= 14 - x
original number 10x + y
reversed number 10y + x
equation 10y +x = 10x +y +36
subsitute for y
10(14-x) + x = 10x +14 - x + 36
140 - 10x + x = 10x +14 - x + 36
x = 5 y = 14 - x
y = 14 - 5 = 9
original number is 10x + y
10(5) + 9 = 59
95
59
To find the original two-digit number, let's call the tens digit "T" and the units digit "U."
The problem states that the sum of the digits is 14, so we can write the equation:
T + U = 14
The problem also states that the number formed by reversing the digits is 36 more than the original number. This means that if we reverse the digits, we get the original number plus 36.
To reverse the digits, we multiply the units digit by 10 and add the tens digit. So, the reversed number can be written as:
10U + T
Now we can write the second equation:
10U + T = original number + 36
To solve the problem, we need to solve this system of equations simultaneously.
First, let's solve the first equation for T:
T = 14 - U
Now, substitute this value of T into the second equation:
10U + (14 - U) = original number + 36
Simplifying:
9U + 14 = original number + 36
Next, we can substitute (original number + 36) with (10U + T):
9U + 14 = 10U + T
Now, substitute T with (14 - U):
9U + 14 = 10U + 14 - U
Simplifying:
9U = U
Now, let's solve for U:
8U = 0
U = 0
Now that we know the units digit is 0, we can substitute this value back into the first equation:
T + 0 = 14
T = 14
Therefore, the original number is 14.
95
86
77
Which of those numbers meet the other criterion?