Question 872376
Let {{{ m }}} = the mother's age now
Let {{{ p }}} = the child's age now
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(1) {{{ m = 3p }}}
(2) {{{ ( m - 7 )*( p - 7 ) = 104 }}}
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(2) {{{ m*p - 7p - 7m + 49 = 104 }}}
(2) {{{ m*p - 7*( p + m ) = 104 - 49 }}}
(2) {{{ m*p - 7*( p + m ) = 55 }}}
Substitute (1) into (2)
(2) {{{ 3p*p - 7*( p + 3p ) = 55 }}}
(2) {{{ 3p^2 - 28p - 55 = 0 }}}
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Solve using the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{ a = 3 }}}
{{{ b = -28 }}}
{{{ c = -55 }}}
{{{ p = (-(-28) +- sqrt( (-28)^2-4*3*(-55) ))/(2*3) }}} 
{{{ p = ( 28 +- sqrt( 784 + 660 ))/6 }}} 
{{{ p = ( 28 +- sqrt( 1444 ))/6 }}} 
{{{ p = ( 28 + 38)/6 }}} ( can't use the negative square root )
{{{ p =  66/6 }}}
{{{ p = 11 }}}
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(1) {{{ m = 3p }}}
(1) {{{ m = 3*11 }}}
(1) {{{ m = 33 }}}
The mother is 33 and the child is 11
check:
(2) {{{ ( m - 7 )*( p - 7 ) = 104 }}}
(2) {{{ ( 33 - 7 )*( 11 - 7 ) = 104 }}}
(2) {{{ 26*4 = 104 }}}
(2) {{{ 104 = 104 }}}
OK