Question 1085222
Let {{{ u }}} = the units digit
Let {{{ t }}} = the tens digit
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(1) {{{ t + u = 15 }}}
(2) {{{ 10u + t = 10t + u - 9 }}}
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(2) {{{ 10u - u + t - 10t = -9 }}}
(2) {{{ -9t + 9u = -9 }}}
(2) {{{ -t + u = -1 }}}
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Add (1) and (2)
(1) {{{ t + u = 15 }}}
(2) {{{ -t + u = -1 }}}
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{{{ 2u = 14 }}}
{{{ u = 7 }}}
and
(1) {{{ t + u = 15 }}}
(1) {{{ t + 7 = 15 }}}
(1) {{{ t = 8 }}}
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The original number is 87
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check:
Interchange the digits: 78
{{{ 78 = 87 - 9 }}}
{{{ 78 = 78 }}}
OK