Question 1059299
Let {{{ x }}} = gallons of 10% solution needed
{{{ 12 - x }}} = gallons of 30% solution needed
{{{ .1x }}} = gallons of pure bleach in 10% solution
{{{ .3*( 12 - x ) }}} = gallons of pure bleach in 30% solution
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{{{ (( .1x + .3*( 12 - x ) )) / 12 = .15 }}}
{{{ (( .1x + 3.6 - .3x )) / 12 = .15 }}}
{{{ (( 3.6 - .2x )) / 12 = .15 }}}
{{{ 3.6 - .2x = .15*12 }}}
{{{ 3.6 - .2x = 1.8 }}}
{{{ .2x = 1.8 }}}
{{{ x = 9 }}}
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9 gallons of 10% solution are needed
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check:
{{{ (( .1*9 + .3*( 12 - 9 ) )) / 12 = .15 }}}
{{{ ( ( .9 + .3*3 )) / 12 = .15 }}}
{{{ ( .9 + .9 ) / 12 = .15 }}}
{{{ 1.8/12 = .15 }}}
{{{ 1.8 = .15*12 }}}
{{{ 1.8 = 1.8 }}}
OK