Question 648118
Let {{{ a }}} = liters of 40% solution needed
Let {{{ b }}} = liters of 20% solution needed
{{{ .4a }}} = liters of salt in 40% solution
{{{ .2b }}} = liters of salt in 20% solution
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(1) {{{ a + b = 50 }}}
(2) {{{ ( .4a + .2b ) / 50 = .25 }}}
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(2) {{{ .4a + .2b = .25*50 }}}
(2) {{{ .4a + .2b = 12.5 }}}
(2) {{{ 4a + 2b = 125 }}}
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Multiply both sides of (1) by {{{2}}}
and subtract (1) from (2)
(2) {{{ 4a + 2b = 125 }}}
(1) {{{ -2a - 2b = -100 }}}
{{{ 2a = 25 }}}
{{{ a = 12.5 }}}
and, since
(1) {{{ a + b = 50 }}}
(1) {{{ 12.5 + b = 50 }}}
(1) {{{ b = 37.5 }}}
12.5 liters of the 40% solution are needed
check:
(2) {{{ ( .4a + .2b ) / 50 = .25 }}}
(2) {{{ ( .4*12.5 + .2*37.5 ) / 50 = .25 }}}
(2) {{{ ( 5 + 7.5 ) / 50 = .25 }}}
(2) {{{ 12.5 = .25*50 }}}
(2) {{{ 12.5 = 12.5 }}}
OK