Question 1100798
Let {{{ a }}} = original numerator
Let {{{ b }}} = original denominator
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given:
(1) {{{ b = 3a + 4 }}}
(2) {{{ ( a - 7 ) / ( b - 7 ) = 2/15 }}}
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(1) {{{ -3a + b = 4 }}}
Multiply both sides of (2) by {{{ 15*( b - 7 ) }}}
(2) {{{ 15*( a - 7 ) = 2*( b - 7 ) }}}
(2) {{{ 15a - 105 = 2b - 14 }}}
(2) {{{ 15a - 2b = 91 }}}
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Multiply both sides of (1) by {{{ 2 }}}
and add the equations
(2) {{{ 15a - 2b = 91 }}}
(1) {{{ -6a + 2b = 8 }}}
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{{{ 9a = 99 }}}
{{{ a = 11 }}}
and
(1) {{{ b = 3a + 4 }}}
(1) {{{ b = 3*11 + 4 }}}
(1) {{{ b = 37 }}}
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The original fraction is 11/37
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check:
(2) {{{ ( a - 7 ) / ( b - 7 ) = 2/15 }}}
(2) {{{ ( 11 - 7 ) / ( 37 - 7 ) = 2/15 }}}
(2) {{{ 4/30 = 2/15 }}}
(2) {{{ 2/15 = 2/15 }}}
OK