Question 1005488
Let {{{ j }}} = John's age now
Let {{{ d }}} = David's age now
given:
(1) {{{ j/d = 6/5 }}}
(2) {{{ ( j+7) / ( d+7 ) = 7/6 }}}
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Multiply both sides of (1) by {{{ d }}}
(1) {{{ j = (6/5)*d }}}
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Multiply both sides of (2) by {{{ 6*( d+7 ) }}}
(2) {{{ 6*( j+7 ) = 7*( d+7 ) }}}
(2) {{{ 6j + 42 = 7d + 49 }}}
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Substitute (1) into (2)
(2) {{{ 6*( (6/5)*d ) + 42 = 7d + 49 }}}
(2) {{{ 6*( (6/5)*d ) - 7d = 7 }}}
Multiply both sides by {{{ 5 }}}
(2) {{{ 36d - 35d = 35 }}}
(2) {{{ d = 35 }}}
and
(1) {{{ j = (6/5)*d }}}
(1) {{{ j = (6/5)*35 }}} 
(1) {{{ j = 42 }}}
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John is 42 and David is 35 
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check:
{{{ 42/35 = 6/5 }}}
{{{ ( 6*7 ) / ( 5*7 ) = 6/5 }}}
OK
and
{{{ ( 42 + 7 ) / ( 35 + 7 ) = 7/6 }}}
{{{ 49/42 = 7/6 }}}
{{{ ( 7*7 ) / ( 6*7 ) = 7/6 }}}
OK