Question 988509
Let {{{ x }}} = gallons of gasoline to be added
so that [ gasoline ] / [ oil ] = {{{ 50/1 }}}
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To start with:
[ gasoline] / [ oil ] = {{{ 30/1 }}}
The gasoline is {{{ 3*( 30/( 30 + 1 ) ) = 90/31 }}} gallons
The oil is {{{ 3*( 1/( 30 + 1 )) = 3/31 }}} gallons
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Note that {{{ 90/31 + 3/31 = 93/31 }}} and
{{{ 93/31 = 3 }}} gallons as it should
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I can say:
{{{ ( 90/31 + x ) / ( 3/31 ) = 50/1 }}}
{{{ 90/31 + x = (3/31)*50 }}}
{{{ x = 150/31 - 90/31 }}}
{{{ x = 60/31 }}}
60/31 gallons of gasoline must be added to mixture
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check:
{{{ ( 90/31 + x ) / ( 3/31 ) = 50/1 }}}
{{{ ( 90/31 + 60/31 ) / ( 3/31 ) = 50/1 }}}
Multiply top anfd bottom of left side by {{{ 31 }}}
{{{ ( 90 + 60 ) / 3 = 50 }}}
{{{ 150 = 150 }}}
OK
hope I got it