Question 515163
Let {{{ x }}} = gallons of 90% antifreeze needed
In words:
( gallons of antifreeze you end up with ) / ( total gallons of solution ) = 80%
{{{ .1*100 = 10 }}} gallons of antifreeze in 10% solution
given:
{{{ 100 + x }}} = total solution
{{{ ( .9x + 10 ) / ( x + 100 ) = .8 }}}
{{{ .9x + 10 = .8*( x + 100 ) }}}
{{{ .9x + 10 = .8x + 80 }}}
{{{ .1x = 80 - 10 }}}
{{{ .1x = 70 }}}
{{{ x = 700 }}}
700 gallons of 90% antifreeze are needed
check answer:
{{{ ( .9*700 + 10 ) / ( 700 + 100 ) = .8 }}}
{{{ ( 630 + 10 ) / 800 = .8 }}}
{{{  640 / 800 = .8 }}}
{{{ 640 = .8*800 }}}
{{{ 640 = 640 }}}
OK