Question 536192
Let {{{ x }}} = ft3 of 45% soil
{{{ .45x }}} = ft3 of sand in 45% soil
given:
{{{ .15*1 }}} = ft3 of sand in 1 ft3 of 15% soil
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In words:
( final cubic ft of sand ) / ( final cubic ft of soil ) = 35%
{{{ ( .45x + .15 ) / ( x + 1 ) = .35 }}}
{{{ .45x + .15 = .35*( x + 1 ) }}}
{{{ .45x + .15 = .35x + .35 }}}
{{{ .1x = .2 }}}
{{{ x = 2 }}}
2 ft3 of soil with 45% sand is needed
check:
{{{ ( .45*2 + .15 ) / ( 2 + 1 ) = .35 }}}
{{{ ( .9 + .15 ) / 3 = .35 }}}
{{{ 1.05 / 3 = .35 }}}
{{{ 1.05 = 1.05 }}}
OK