Question 559912
Let {{{ a }}} = liters of water to be added
Let {{{ b }}} = liters of 50% soap solution to be added
given:
{{{ .05*1 = .05 }}} liters of soap in 5% solution
{{{ .5b }}} =liters of soap in  50% solution
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(1) {{{ ( .05 + .5b ) / ( a + b + 1 ) = .08 }}}
(2) {{{ a + b + 1 = 2 }}}
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(1) {{{ ( .05 + .5b ) / ( a + b + 1 ) = .08 }}}
(1) {{{ .05 + .5b = .08*( a + b + 1 ) }}}
(1) {{{ .05 + .5b = .08a + .08b + .08 }}}
(1) {{{ .08a - .42b = -.03 }}}
(1) {{{ 8a - 42b = -3 }}}
and
(2) {{{ a + b = 1 }}}
(2) {{{ a = 1- b }}}
and
(1) {{{ 8*( 1 - b ) - 42b = -3 }}}
(1) {{{ 8 - 8b - 42b = -3 }}}
(1) {{{ -50b = -11 }}}
(1) {{{ b = .22 }}}
and
{{{ a = 1 - .22 }}}
{{{ a = .78 }}}
.78 liters of water and .22 liters of 50% soap
solution must be added
check answer:
(1) {{{ ( .05 + .5*.22 ) / ( .78 + .22 + 1 ) = .08 }}}
(1) {{{ .16  / 2 = .08 }}}
(1) {{{ .16 = .16 }}}
OK