Answer:
The number is 62
Step-by-step explanation:
Let the digits of the number be T and U;
A 2 digit number is represented as: 10T + U
So,
[tex]T + U = 8[/tex]
[tex]10T + U - (10U + T) = 10 + 10U + T[/tex]
Required
Find the digit
Make U the subject in the first equation
[tex]U = 8 - T[/tex]
Substitute 8 - T for U in the second
[tex]10T + U - (10U + T) = 10 + 10U + T[/tex]
[tex]10T + 8 - T - (10*(8-T) + T) = 10 + 10(8 - T) + T[/tex]
[tex]10T + 8 - T - (80-10T + T) = 10 + 80 - 10T+ T[/tex]
[tex]10T + 8 - T -80+10T - T = 10 + 80 - 10T+ T[/tex]
Collect Like Terms
[tex]10T + 10T - T- T + 8 -80 = 10 + 80 - 10T+ T[/tex]
[tex]18T -72 = 90 - 9T[/tex]
[tex]9T + 18T = 90 + 72[/tex]
[tex]27T = 162[/tex]
[tex]T = 162/27[/tex]
[tex]T = 6[/tex]
Recall that:
[tex]U = 8 - T[/tex]
[tex]U = 8 - 6[/tex]
[tex]U = 2[/tex]
Hence, the number is 62
