Question 943893
Let {{{ s }}} = the son's age today
{{{ 4s }}} = the father's age today
{{{ s - 6 }}} was the son's age 6 yrs ago
{{{ 4s - 6 }}} was the father's age 6 yrs ago
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The product of the ages was:
{{{ ( s - 6 )*( 4s - 6 ) = 252 }}}
{{{ 4s^2 - 24s - 6s + 36 = 252 }}}
{{{ 4s^2 - 30s - 216 }}}
{{{ 2s^2 - 15s - 108 = 0 }}}
use quadratic formula:
{{{ s = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 2 }}}
{{{ b = -15 }}}
{{{ c = -108 }}}
{{{ s = ( -(-15) +- sqrt( (-15)^2 - 4*2*(-108) )) / (2*2) }}}
{{{ s = ( 15 +- sqrt( 225 + 864)) / 4 }}}
{{{ s = ( 15 +- sqrt( 1089)) / 4 }}}
{{{ s = ( 15 + 33 ) / 4 }}}  ( take the positive square root )
{{{ s = 48/4 }}}
{{{ s = 12 }}}
and
{{{ 4s = 4*12 }}}
{{{ 4s = 48 }}}
The son is 12 and the father is 48
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check:
{{{ ( s - 6 )*( 4s - 6 ) = 252 }}}
{{{ ( 12 - 6 )*( 48 - 6 ) = 252 }}}
{{{ 6*42 = 252 }}}
{{{ 252 = 252 }}}
OK