Question 409852
Let the units digit = {{{a}}}
Let the tens digit = {{{b}}}
the number is: {{{10b + a}}}
the number with reversed digits is: {{{10a + b}}}
given:
(1) {{{a + b = 7}}}
(2) {{{10a + b = 2*(10b + a) + 2}}} 
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(2) {{{10a + b = 20b + 2a + 2}}}
(2) {{{8a - 19b = 2}}}
Multiply both sides of (1) by {{{8}}}
and subtract (1) from (2)
(2) {{{8a - 19b = 2}}}
(1) {{{-8a - 8b = -56}}}
{{{-27b = -54}}}
{{{b = 2}}}
and, since
(1) {{{a + b = 7}}}
{{{a = 5}}}
The original number is {{{10b + a }}} = 25
check answer:
(2) {{{10a + b = 2*(10b + a) + 2}}} 
(2) {{{10*5 + 2 = 2*(10*2 + 5) + 2}}}
(2) {{{52 = 2*25 + 2}}}
(2) {{{52 = 52}}}
OK