Question 698705
Let the 10s digit = {{{ a }}}
Let the units digit = {{{ b }}}
Note that the actual value of the number is
{{{ 10a + b }}}
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given:
(1) {{{ 10a + b = 6*( a + b ) }}}
(2) {{{ 10b + a = 4*( b + a ) + 9 }}}
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(1) {{{ 10a + b = 6a + 6b }}}
(1) {{{ 10a - 6a = 6b - b }}}
(1) {{{ 4a = 5b }}}
(1) {{{ a = (5/4)*b }}}
and
(2) {{{ 10b + a = 4*( b + a ) + 9 }}}
(2) {{{ 10b + a = 4b + 4a + 9 }}}
(2) {{{ 4a - a = 10b - 4b - 9 }}}
(2) {{{ 3a = 6b - 9 }}}
By substitution:
(2) {{{ 3*(5/4)*b = 6b - 9 }}}
(2) {{{ 15b = 24b - 36 }}}
(2) {{{ 9b = 36 }}}
(2) {{{ b = 4 }}}
and
(1) {{{ a = (5/4)*b }}}
(1) {{{ a = (5/4)*4 }}}
(1) {{{ a = 5 }}}
The original number is 54
Whatever you did was pretty good.