Question 1074171
Let {{{ x }}} = cubic yds of soil with 10% sand
{{{ .1x }}} = cubic yds of sand in the 10% soil
{{{ .4*.5 = .2 }}} yd3 of sand in the 40% soil
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{{{ ( .1x + .2 ) / ( x + .5 ) = .16 }}}
{{{ .1x + .2 = .16*( x + .5 ) }}}
{{{ .1x + .2 = .16x + .08 }}}
{{{ .06x = .12 }}}
{{{ x = 2 }}}
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2 cubic yds of soil with 10% sand needs to be added
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check:
{{{ ( .1x + .2 ) / ( x + .5 ) = .16 }}}
{{{ ( .1*2 + .2 ) / ( 2 + .5 ) = .16 }}}
{{{ ( .2 + .2 ) / 2.5 = .16 }}}
{{{ .4 = .16 * 2.5 }}}
{{{ .4 = .4 }}}
OK