Question 992390
Let {{{ a }}} = kg of 22% copper alloy
Let {{{ b }}} = kg of 49% copper alloy
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(1) {{{ a + b = 12 }}}
(2) {{{ ( .22a + .49b ) / 12 = .38 }}}
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(2) {{{ .22a + .49b = .38*12 }}}
(2) {{{ .22a + .49b = 4.56 }}}
(2) {{{ 22a + 49b = 456 }}}
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Multiply both sides of (1) by 22 and
subtract (1) from (2)
(2) {{{ 22a + 49b = 456 }}}
(1) {{{ -22a - 22b = -264 }}}
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{{{ 27b = 192 }}}
{{{ b = 7.111 }}}
and
(1) {{{ a +7.111 = 12 }}}
(1) {{{ a = 4.888 }}}
4.889 kg of 22% copper alloy is needed
7.111 kg of 49% copper alloy is needed
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check:
(2) {{{ ( .22a + .49b ) / 12 = .38 }}}
(2) {{{ ( .22*4.889 + .49*7.111 ) / 12 = .38 }}}
(2) {{{ ( 1.07558 + 3.48439 ) / 12 = .38 }}}
(2) {{{ 4.55997 = .38*12 }}}
(2) {{{ 4.55997 = 4.56 }}}
close enough -OK