Question 935490
Let the tens digit = {{{ t }}}
Let the units digit = {{{ u }}}
The value of the number is:
{{{ 10t + u }}}
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(1) {{{ t = u - 2 }}}
(2) {{{ 3*( 10t + u ) + ( 6/7 )*( 10u + t ) = 108 }}}
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(2) {{{ 30t + 3u + ( 60/7 )*u + ( 6/7 )*t = 108 }}}
(2) {{{ 210t + 21u + 60u + 6t = 108*7 }}}
(2) {{{ 216t + 81u = 756 }}}
(2) {{{ 24t + 9u = 84 }}}
(2) {{{ 8t + 3u = 28 }}}
and, by substitution:
(2) {{{ 8*( u - 2 ) + 3u = 28 }}}
(2) {{{ 8u - 16 + 3u = 28 }}}
(2) {{{ 11u = 44 }}}
(2) {{{ u = 4 }}}
and, since
(1) {{{ t = u - 2 }}}
(1) {{{ t = 4 - 2 }}}
(1) {{{ t = 2 }}}
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The number is {{{ 24 }}}
The sum of the digits is {{{ 6 }}}
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check answer:
(2) {{{ 3*( 10t + u ) + ( 6/7 )*( 10u + t ) = 108 }}}
(2) {{{ 3*( 10*2 + 4 ) + ( 6/7 )*( 10*4 + 2 ) = 108 }}}
(2) {{{ 3*24 + ( 6/7 )*42 = 108 }}}
(2) {{{ 72 + 36 = 108 }}}
(2) {{{ 108 = 108 }}}
OK