Question 891887
Let {{{ a }}} = ml of 30% solution needed
Let {{{ b }}} = ml of 15% solution needed
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(1) {{{ a + b = 300 }}}
(2) {{{ ( .3a + .15b ) / 300 = .2 }}}
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(2) {{{ .3a + .15b = .2*300 }}}
(2) {{{  .3a + .15b = 60 }}}
(2) {{{ 30a + 15b = 6000 }}}
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Multiply both sides of (1) by {{{ 15 }}}
and subtract (1) from (2)
(2) {{{ 30a + 15b = 6000 }}}
(1) {{{ -15a - 15b = 4500 }}}
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{{{ 15a = 1500 }}}
{{{ a = 100 }}}
and, since
(1) {{{ a + b = 300 }}}
(1) {{{ b = 200 }}}
100 ml of 30% solution is needed
200 ml of 15% solution is needed
check:
(2) {{{ ( .3a + .15b ) / 300 = .2 }}}
(2) {{{ ( .3*100 + .15*200 ) / 300 = .2 }}}
(2) {{{ 30 + 30 = .2*300 }}}
(2) {{{ 60 = 60 }}}
OK