Question 854679
Each slice costs {{{ 18/8 = 9/4 }}}
{{{ 9/4 = 2.25 }}}
{{{ b = a + (2/3)*a }}}
{{{ b = (5/3)*a }}}
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{{{ a + b = 18 }}}
By substitution:
{{{ a + (5/3)*a = 18 }}}
{{{ (8/3)*a = 18 }}}
{{{ a = (3/8)*18 }}}
{{{ a = 27/4 }}}
{{{ a = 6.75 }}} ( 3 slices )
and
{{{ a + b = 18 }}}
{{{ b = 72/4 - 27/4 }}}
{{{ b = 45/4 }}}
{{{ b = 11.25 }}} ( 5 slices )
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A pays $6.75
B pays $11.25
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check:
{{{ b = (5/3)*a }}}
{{{ 45/4 = ( 5/3)*( 27/4 ) }}}
Multiply both sides by {{{ 12 }}}
{{{ 45*3 = 5*27 }}}
Divide both sides by {{{ 15 }}}
{{{ 9 = 9 }}}
OK