Question 1061149
Let {{{ a }}} = ml of 25% mixture needed
Let {{{ b }}} = ml of 60% mixture needed
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(1) {{{ a + b = 420 }}}
(2) {{{ ( .25a + .6b ) / 420 = .35 }}}
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(2) {{{ .25a + .6b = .35*420 }}}
(2) {{{ .25a + .6b = 147 }}}
(2) {{{ 25a + 60b = 14700 }}}
(2) {{{ 5a + 12b = 2940 }}}
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Multiply both sides of (1) by {{{ 5 }}}
and subtract (1) from (2)
(2) {{{ 5a + 12b = 2940 }}}
(1) {{{ -5a - 5b = -2100 }}}
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{{{ 7b = 840 }}}
{{{ b = 120 }}}
and
(1) {{{ a + 120 = 420 }}}
(1) {{{ a = 300 }}}
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300 ml of 25% mixture is needed
120 ml of 60% mixture is needed
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check:
(2) {{{ ( .25a + .6b ) / 420 = .35 }}}
(2) {{{ ( .25*300 + .6*120 ) / 420 = .35 }}}
(2) {{{ ( 75 + 72 ) / 420 = .35 }}}
(2) {{{ 147 = .35*420 }}}
(2) {{{ 147 = 147 }}}
OK