Question 980590
Let {{{ a }}} = kg of 30% alloy needed
Let {{{ b }}} = kg of 70% alloy needed
{{{ .48*20 = 9.6 }}} kg of nickel in 48% alloy
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(1) {{{ a + b = 20 }}}
(2) {{{ ( .3a + .7b ) / 20 = .48 }}}
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(2) {{{ .3a + .7b = 9.6 }}}
(2) {{{ 3a + 7b = 96 }}}
Multiply both sides of (1) by {{{ 3 }}} and
subtract (1) from (2)
(2) {{{ 3a + 7b = 96 }}}
(1) {{{ -3a - 3b = -60 }}}
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{{{ 4b = 36 }}}
{{{ b = 9 }}}
and
(1) {{{ a + b = 20 }}}
(1) {{{ a = 11 }}}
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11 kg of 30% alloy is needed
9 kg of 70% alloy is needed
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check:
(2) {{{ ( .3a + .7b ) / 20 = .48 }}}
(2) {{{ ( .3*11 + .7*9 ) / 20 = .48 }}}
(2) {{{ ( 3.3 + 6.3 ) / 20 = .48 }}}
(2) {{{ 9.6 = 20*.48 }}}
(2) {{{ 9.6 = 9.6 }}}
OK