Question 724360
Let {{{ u }}} = the units digit
Let {{{ t }}} = the tens digit
given:
(1) {{{ t = u + 5 }}}
(2) {{{ ( 10t + u ) / ( t + u ) = 7 + 6/( t + u ) }}}
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Substitute (1) into (2)
(2) {{{ ( 10*( u + 5 ) + u ) / ( u + 5 + u ) = 7 + 6/( u + 5 + u ) }}}
(2) {{{ ( 10u + 50 + u ) / ( 2u + 5 ) = 7 + 6/( 2u + 5 ) }}}
Multiply both sides by {{{ 2u + 5 }}}
(2) {{{ 11u + 50 = 7*( 2u + 5 ) + 6 }}}
(2) {{{ 11u + 50 = 14u + 35 + 6 }}}
(2) {{{ 3u = 9 }}}
(2) {{{ u = 3 }}}
and, since
(1) {{{ t = u + 5 }}}
(1) {{{ t = 3 + 5 }}}
(1) {{{ t = 8 }}}
The number is 83
check answer:
(2) {{{ ( 10t + u ) / ( t + u ) = 7 + 6/( t + u ) }}}
(2) {{{ ( 10*8 + 3 ) / ( 8 + 3 ) = 7 + 6/( 8 + 3 ) }}}
(2) {{{ 83/11 = 7 + 6/11 }}}
(2) {{{ 83 = 77 + 6 }}}
(2) {{{ 83 = 83 }}}
OK