Question 1151235
Let {{{ x }}} = gallons of 40% alcohol needed
{{{ 30 - x }}} = gallons of 70% alcohol needed
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{{{ ( .4x + .7*( 30 - x ) ) / 30 = .52 }}}
{{{ ( .4x + 21 - .7x ) / 30 = .52 }}}
{{{  21 - .3x = 15.6 }}}
{{{ .3x = 5.4 }}}
{{{ x = 18 }}}
and
{{{ 30 - x = 12 }}}
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18 gallons of 40% alcohol are needed
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check:
{{{ ( .4x + .7*( 30 - x ) ) / 30 = .52 }}}
{{{ ( .4*18 + .7*12 ) / 30 = .52 }}}
{{{ ( 7.2 + 8.4 ) / 30 = .52 }}}
{{{ 15.6 / 30 = .52 }}}
{{{ 15.6 = 15.6 }}}
OK