Question 556152
Let {{{ m }}} = man's age now
Let {{{ d }}} = Daughter's age now
given:
(1) {{{ m = 5d }}}
(2) {{{ ( m - 6 )*( d - 6 ) = 324 }}}
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Substitute (1) into (2)
(2) {{{ ( 5d - 6 )*( d - 6 ) = 324 }}}
(2) {{{ 5d^2 - 6d - 30d + 36 = 324 }}}
(2) {{{ 5d^2 - 36d - 288 = 0 }}}
Use quadratic formula
{{{d = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = 5 }}}
{{{ b = -36 }}}
{{{ c = -288 }}}
{{{ d = (-(-36) +- sqrt( (-36)^2-4*5*(-288) ))/(2*5) }}}
{{{ d = ( 36 +- sqrt( 1296 + 5760 ))/ 10 }}}
{{{ d = ( 36 +- sqrt( 7056 ))/ 10 }}}
{{{ d = ( 36 +- 84 )/ 10 }}}
{{{ d = ( 36 + 84 ) / 10 }}}
{{{ d = 120/10 }}}
{{{ d = 12 }}}
and,
(1) {{{ m = 5d }}}
(1) {{{ m = 5*12 }}}
(1) {{{ m = 60 }}}
The man is 60 and the daughter is 12
check:
(2) {{{ ( m - 6 )*( d - 6 ) = 324 }}}
(2) {{{ ( 60 - 6 )*( 12 - 6 ) = 324 }}}
(2) {{{ 54*6 = 324 }}}
(2) {{{ 324 = 324 }}}
OK