Question 831096
Let {{{ t }}} = the tens digit
Let {{{ u }}} = the units digit
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(1) {{{ t/u = 2/3 }}}
(2) {{{ 10t + u + 27 = 10u + t }}}
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(2) {{{ 10t - t + 27 = 10u - u }}}
(2) {{{ 9u - 9t = 27 }}}
(2) {{{ u - t = 3 }}}
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(1) {{{ t = (2/3)*u }}}
Substitute (1) into (2)
(2) {{{ u - (2/3)*u = 3 }}}
(2) {{{ (1/3)*u = 3 }}}
(2) {{{ u = 9 }}}
and
(2) {{{ u - t = 3 }}}
(2) {{{ t = u - 3 }}}
(2) {{{ t = 9 - 3 }}}
(2) {{{ t = 6 }}}
The original number is 69
check:
(2) {{{ 10t + u + 27 = 10u + t }}}
(2) {{{ 10*6 + 9 + 27 = 10*9 + 6 }}}
(2) {{{ 69 + 27 = 90 + 6 }}}
(2) {{{ 96 = 96 }}}
OK