Question 1054174
Let {{{ a }}} = ounces of the 20% solution needed
Let {{{ b }}} = ounces of the 40% solution needed
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(1) {{{ a + b = 30 }}}
(2) {{{ ( .2a + .4b ) / 30 = .28 }}}
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(2) {{{ .2a + .4b = .28*30 }}}
(2) {{{ .2a + .4b = 8.4 }}}
(2) {{{ 2a + 4b = 84 }}}
Multiply both sides of (1) by {{{ 2 }}} and
subtract (1) from (2)
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(2) {{{ 2a + 4b = 84 }}}
(1) {{{ -2a - 2b = -60 }}}
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{{{ 2b = 24 }}}
{{{ b = 12 }}}
and
(1) {{{ a + 12 = 30 }}}
(1) {{{ a = 18 }}}
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18 ounces of the 20% solution are needed
12 ounces of the 40% solution are needed
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check:
(2) {{{ ( .2a + .4b ) / 30 = .28 }}}
(2) {{{ ( .2*18 + .4*12 ) / 30 = .28 }}}
(2) {{{ ( 3.6 + 4.8 ) / 30 = .28 }}}
(2) {{{ 8.4 = .28*30 }}}
(2) {{{ 8.4 = 8.4 }}}
OK