Question 663153
The fractions of the $900K that each gets
add up to {{{ 1 }}}
Let {{{ a }}} = Maria's fraction
Let {{{ b }}} = Lorna's fraction
Let {{{ c }}} = Fe's fraction
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given:
{{{ b = (3/5)*a }}}
{{{ c = (1/2)*a }}}
{{{ a + b + c = 1 }}}
By substitution:
{{{ a + (3/5)*a + (1/2)*a = 1 }}}
{{{ (10/10)*a + (6/10)*a + (5/10)*a = 1 }}}
{{{ (21/10)*a = 1 }}}
{{{ a = 10/21 }}}
and
{{{ b = (3/5)*a }}}
{{{ b = (3/5)*(10/21) }}}
{{{ b = 6/21 }}}
and
{{{ c = (1/2)*a }}}
{{{ c = (1/2)*(10/21) }}}
{{{ c = 5/21 }}}
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Maria receives {{{ (10/21)*900000 = 428571.42 }}}
Lorna receives {{{ (6/21)*900000 = 257142.85 }}}
Fe receives {{{ (5/21)*900000 = 214285.71 }}}
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check:
Lorna is to receive 3/5 of what Maria gets
{{{ 257142.85 = (3/5)* 428571.42 }}}
{{{ 257142.85 = 257142.85 }}}
Fe gets 1/2 of what Maria gets
{{{ 214285.71 = (1/2)*428571.42 }}}
{{{ 214285.71 = 214285.71 }}}
and
{{{  428571.42 + 257142.85 + 214285.71 = 900000 }}}
{{{ 899999.98 = 900000 }}}
I'm off by .02 due to rounding off of my calculator, I guess