Question 1094915
Let {{{ a - 2 }}} = the girl's age now
Let {{{ b - 2 }}} = her younger brother's age now
Let {{{ c - 2 }}} = her older brother's age now
( I did this to make the 3rd equation simpler )
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With 3 unknowns, I need 3 equations
(1) {{{ a - 2 = b - 2 + 5 }}}
(2) {{{ a - 2 = c - 2 - 3 }}}
(3) {{{ ( b - 2 + 2 )*( c - 2 + 2 ) = 12*( a - 2 + 2 ) }}}
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(3) {{{ b*c = 12a }}}
and
(1) {{{ a - 2 = b + 3 }}}
(1) {{{ a - b = 5 }}}
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(2) {{{ a - 2 = c - 5 }}}
(2) {{{ c = a + 3 }}}
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Plug (2) into (3)
(3) {{{ b*( a + 3 ) = 12a }}}
(3) {{{ b = 12a / ( a + 3 ) }}}
Plug this into (1)
(1) {{{ a - ( 12a )/( a + 3 ) = 5 }}}
(1) {{{ a*( a + 3 ) -12a = 5*( a + 3 ) }}}
(1) {{{ a^2 + 3a - 12a = 5a + 15 }}}
(1) {{{ a^2 - 14a - 15 = 0 }}}
(1) {{{ ( a - 15 )*( a + 1 ) = 0 }}} ( by looking at it )
{{{ a = 15 }}} ( can't have a negative age )
and
(2) {{{ c = a + 3 }}}
(2) {{{ c = 18 }}}
and
(1) {{{ a - b = 5 }}}
(1) {{{ 15 - b = 5 }}}
(1) {{{ b = 10 }}}
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{{{ a - 2 = 13 }}}
{{{ b - 2 = 8 }}}
{{{ c - 2 = 16 }}}
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The girl is 13
Her younger brother is 8
Her older brother is 16
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check:
The girl is:
5 yrs older than younger brother YES
3 yrs younger than older brother YES
and
{{{ ( 8 + 2 )*( 16 + 2 ) = 12*( 13 + 2 ) }}}
{{{ 10*18 = 12*15 }}}
{{{ 180 = 180 }}}
OK