Question 544540
Let {{{ a }}} = tens digit
Let {{{ b }}} = units digit
{{{ 10a + b }}} = the value of the number
given:
(1) {{{ 10b + a = 10a + b + 27 }}}
(2) {{{ b = 3a + 1 }}}
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(1) {{{ -9a + 9b = 27 }}}
(1) {{{ -a + b = 3 }}}
(2) {{{ -3a + b = 1 }}}
Subtract (2) from (1)
(1) {{{ -a + b = 3 }}}
(2) {{{ 3a - b = -1 }}}
{{{ 2a = 2 }}}
{{{ a = 1 }}}
and, since
(2) {{{ b = 3a + 1 }}}
(2) {{{ b = 3*1 + 1 }}}
(2) {{{ b = 4 }}}
The number is 14
Check answer:
(1) {{{ 10b + a = 10a + b + 27 }}}
(1) {{{ 10*4 + 1 = 10*1 + 4 + 27 }}}
(1) {{{ 41 = 14 + 27 }}}
(1) {{{ 41 = 41 }}}
OK