The sum of the digits of a two digit number is 14. When the digits are reversed, the new number is 36 less than the original number. Find the original number. Check your answer.

Here is the algebraic solution: T is the tens digit O is the ones digit T+O = 14 So

Step-by-step explanation:O = 14 - T < this is the first equation

The original number is 10*T + O

If the digits are reversed the original number is increased by 18.

The number if the digits are reversed is:

10*O + T = 10*T + O + 18

10*(14-T) + T = 10*T + (14-T) + 18 <--- substitutes O with 14-T per first equation above in bold

140 - 10T + T = 10T + 14 - T + 18 <--- distributive left side

140 - 9T = 9T + 32

140 = 9T + 9T + 32

140 - 32 = 9T + 9T

108 = 18T

108/18 = T

T= 6

THe tens digit is 6.

The ones digit must be 8.

Reversing 86 - 68 = 18

The original number is 68.

step-by-step explanation: