Question 567574
let the tens digit = {{{ a }}}
Let the units digit = {{{ b }}}
The actual number is {{{ 10a + b }}}
The number with the digits reversed is {{{ 10b + a }}}
given:
(1) {{{ a + b = 9 }}}
(2) {{{ ( 10b + a ) / ( 10a + b ) = 3/8 }}}
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Multiply both sides of (2) by {{{ 8*( 10a + b ) }}}
(2) {{{ 8*(10b + a) = 3*( 10a + b ) }}}
(2) {{{ 80b + 8a = 30a + 3b }}}
(2) {{{ 22a - 77b = 0 }}}
(2) {{{ 22a = 77b }}}
(2) {{{ a = (77/22)*b }}}
(2) {{{ a = (7/2)*b }}}
Substitute (2) into (1)
(1) {{{ (7/2)*b + b = 9 }}}
(1) {{{ 7b + 2b = 18 }}}
(1) {{{ 9b = 18 }}}
(1) {{{ b = 2 }}}
and, since
(1) {{{ a+ b = 9 }}}
(1) {{{ a + 2 = 9 }}}
(1) {{{ a = 7 }}}
The original number is 72
check answer:
(2) {{{ ( 10b + a ) / ( 10a + b ) = 3/8 }}}
(2) {{{ ( 10*2 + 7 ) / ( 10*7 + 2 ) = 3/8 }}}
(2) {{{ 27 / 72 = 3/8 }}}
Multiply both sides by {{{ 72 }}}
(2) {{{ 27 = 3*9 }}}
(2) {{{ 27 = 27 }}}
OK
Note that the answer {{{ 77 }}} is impossible,
since the digits have to add up to {{{9}}}