Question 390239
Let the 2 digit number = {{{10a + b}}}
where {{{a}}} and {{{b}}} are the digits
given:
(1) {{{10a + b = 4*(a + b)}}}
(2) {{{10a + b + 27 = 10b + a}}}
Note that the number with the digits reversed is {{{10b + a}}}
--------------------------
From (1):
{{{10a + b = 4a + 4b}}}
{{{6a = 3b}}}
{{{2a = b}}}
From (2):
 {{{10a + b + 27 = 10b + a}}}
Using substitution:
{{{10a + 2a + 27 = 10*2a + a}}}
{{{12a + 27 = 20a  + a}}}
{{{9a = 27}}}
{{{a = 3}}}
and
{{{b = 2a}}}
{{{b = 6}}}
The number is 36
check answer:
(1) {{{10a + b = 4*(a + b)}}}
{{{10*3 + 6 = 4*(3 + 6)}}}
{{{36 = 4*9}}}
{{{36 = 36}}}
OK
(2) {{{10a + b + 27 = 10b + a}}}
 {{{10*3 + 6 + 27 = 10*6 + 3}}}
{{{63 = 60 + 3}}}
{{{63 = 63}}}
OK