Question

The sum of the digits of a two-digit number is 8. The difference between the number and the reversed number is 10 more than the reversed number. Find the number.

Answer 1

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,

$T + U = 8$

$10T + U - (10U + T) = 10 + 10U + T$

Required

Find the digit

Make U the subject in the first equation

$U = 8 - T$

Substitute 8 - T for U in the second

$10T + U - (10U + T) = 10 + 10U + T$

$10T + 8 - T - (10*(8-T) + T) = 10 + 10(8 - T) + T$

$10T + 8 - T - (80-10T + T) = 10 + 80 - 10T+ T$

$10T + 8 - T -80+10T - T = 10 + 80 - 10T+ T$

Collect Like Terms

$10T + 10T - T- T + 8 -80 = 10 + 80 - 10T+ T$

$18T -72 = 90 - 9T$

$9T + 18T = 90 + 72$

$27T = 162$

$T = 162/27$

$T = 6$

Recall that:

$U = 8 - T$

$U = 8 - 6$

$U = 2$

Hence, the number is 62