Question 557651
You had the right equations
Let {{{ a }}} = the tens digit
Let {{{ b }}} = units digit
given:
(1) {{{ 10a + b = 8*( a + b ) }}}
(2) {{{ 10a + b + 10b + a = 99 }}}
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(1) {{{ 10a + b = 8a + 8b }}}
(1) {{{ 10a - 8a = 8b - b }}}
(1) {{{ 2a = 7b }}}
(1) {{{ a = (7/2)*b }}}
and
(2) {{{ 11a + 11b = 99 }}}
(2) {{{ a + b = 9 }}}
Substitute (1) into (2)
(2) {{{ (7/2)*b + b = 9 }}}
(2) {{{ (9/2)*b = 9 }}}
(2) {{{ (1/2)*b = 1 }}}
(2) {{{ b = 2 }}}
and, since
(1) {{{ a = (7/2)*b }}}
(1) {{{ a = (7/2)*2 }}}
(1) {{{ a = 7 }}}
The number is 72
check:
(1) {{{ 10a + b = 8*( a + b ) }}}
(1) {{{ 10*7 + 2 = 8*( 7 + 2 ) }}}
(1) {{{ 72 = 72 }}}
and
(2) {{{ 10a + b + 10b + a = 99 }}}
(2) {{{ 10*7 + 2 + 10*2 + 7 = 99 }}}
(2) {{{ 72 + 27 = 99 }}}
(2) {{{ 99 = 99 }}}
OK