Question 990808
Let {{{ t }}} = the tens digit
Let {{{ u }}} = the units digit
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(1) {{{ t = u - 3 }}}
(2) {{{ ( 10t + u ) / ( t + u ) = 4 + 3/( t + u ) }}}
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Multiply both sides of (2) by {{{ t + u }}}
(2) {{{ 10t + u = 4*( t + u ) + 3 }}}
(2) {{{ 10t + u = 4t + 4u + 3 }}}
(2) {{{ 6t - 3u = 3  }}}
(2) {{{ 2t - u = 1 }}}
and
(1) {{{ -t + u = 3 }}}
Add (1) and (2)
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{{{ t = 4 }}}
and
(1) {{{ t = u - 3 }}}
(1) {{{ 4 = u - 3 }}}
(1) {{{ u = 7 }}}
The number is 47
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check:
(2) {{{ ( 10t + u ) / ( t + u ) = 4 + 3/( t + u ) }}}
(2) {{{ ( 10*4 +7 ) / ( 4 + 7 ) = 4 + 3/( 4 + 7 ) }}}
(2) {{{ 47 / 11 = 4 + 3/11 }}}
(2) {{{ 47 = 44 + 3 }}}
(2) {{{ 47 = 47 }}}
OK