Question 553942
Let {{{ x }}} = gallons of 50% antifreeze needed
{{{ .5x }}} = gallons of antifreeze in 50% solution
given:
{{{ .25*90 = 22.5 }}} = gallons of antifreeze in 90% solution
(1) {{{ ( .5x + 22.5 ) / ( x + 90 ) = .4 }}}
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{{{ .5x + 22.5 = .4*( x + 90 ) }}}
{{{ .5x + 22.5 = .4x + 36 }}}
{{{ .1x = 36 - 22.5 }}}
{{{ .1x = 13.5 }}}
{{{ x = 135 }}}
135 gallons of 50% antifreeze are needed
check answer:
(1) {{{ ( .5*135 + 22.5 ) / ( 135 + 90 ) = .4 }}}
(1) {{{ ( 67.5 + 22.5 ) / 225 = .4 }}}
(1) {{{ 90 = .4*225 }}}
(1) {{{ 90 = 90 }}}
OK