Question 922952
Let {{{ c }}} = the cost in CENTS of 1 quart of orange juice
{{{ c - 100 }}} = the cost in CENTS of 1 quart of grape juice
-----------------
Convert quantities of juice to multiples of {{{ 1/2 }}}
{{{ (5/2)*c + (3/2)*( c - 100 ) = 1250 }}} ( all in CENTS )
Multiply both sides by {{{ 2 }}}
{{{ 5c + 3*( c - 100 ) = 2500 }}}
{{{ 5c + 3c - 300 = 2500 }}}
{{{ 8c = 2800 }}}
{{{ c = 350 }}} cents
{{{ c - 100 = 250 }}} cents
1 quart of orange juice cost $3.50
1 quart of grape juice costs $2.50
--------------
check:
{{{ (5/2)*c + (3/2)*( c - 100 ) = 1250 }}}
{{{ (5/2)*350 + (3/2)*( 350 - 100 ) = 1250 }}} 
{{{ (5/2)*350 + (3/2)*250 = 1250 }}}
Divide both sides by {{{ 50 }}}
{{{ 35/2 + 15/2 = 25 }}}
{{{ 35 + 15 = 50 }}}
{{{ 50 = 50 }}}
OK