Question 197870
Call the tens digit {{{a}}}
Call the units digit {{{b}}}
The number is {{{10a + b}}}
given:
(1) {{{a = b + 3}}}
(2) {{{10a + b = 6*(a + b) + 8}}}
Substitute (1) in (2)
(2) {{{10*(b + 3) + b = 6*(b + 3 + b) + 8}}}
{{{10b + 30 + b = 6b + 18 + 6b + 8}}}
{{{11b + 30 = 12b + 26}}}
{{{b = 4}}}
And, from (1)
{{{a = 4 + 3}}}
{{{a = 7}}}
The number is 74
check answer:
(2) {{{10a + b = 6*(a + b) + 8}}}
{{{10*7 + 4 = 6*(7 + 4) + 8}}}
{{{74 = 6*11 + 8}}}
{{{74 = 74}}}