Question 566626
Let {{{ a }}} = the tens digit
Let {{{ b }}} = the units digit
The number is {{{ 10a + b }}}
given:
(1) {{{ a + b = 8 }}}
The number with the digits interchanged is
{{{ 10b + a }}}
(2) {{{ 10b + a = 8b + 14 }}}
(2) {{{ a + 10b - 8b = 14 }}}
(2) {{{ a + 2b = 14 }}}
Subtract (1) from (2)
(2) {{{ a + 2b = 14 }}}
(1) {{{ -a - b = -8 }}}
{{{ b = 6 }}}
and
(1) {{{ a + b = 8 }}}
(1) {{{ a + 6 = 8 }}}
(1) {{{ a = 8 - 6 }}}
(1) {{{ a = 2 }}}
The number is 26
check answer:
(2) {{{ a + 2b = 14 }}}
(2) {{{ 2 + 2*6 = 14 }}}
(2) {{{ 2 + 12 = 14 }}}
OK