Question 1097016
Let {{{ a }}} = mL of 5% solution needed
Let {{{ b }}} = mL of 2% solution needed
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(1) {{{ a + b = 60 }}} mL
(2) {{{ ( .05a + .02b ) / 60 = .03 }}}
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(2) {{{ .05a + .02b = .03*60 }}}
(2) {{{ .05a + .02b = 1.8 }}}
(2) {{{ 5a + 2b = 180 }}}
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Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 5a + 2b = 180 }}}
(1) {{{ -2a - 2b = -120 }}}
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{{{ 3a = 60 }}}
{{{ a = 20 }}}
and
(1) {{{ 20 + b = 60 }}}
(1) {{{ b = 40 }}}
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20 mL of 5% solution are needed
40 mL of 2% solution are needed
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check:
(2) {{{ ( .05a + .02b ) / 60 = .03 }}}
(2) {{{ ( .05*20 + .02*40 ) / 60 = .03 }}}
(2) {{{ ( 1 + .8 ) / 60 = .03 }}}
(2) {{{ 1.8 = .03*60 }}}
(2) {{{ 1.8 = 1.8 }}}
OK