Question 820479
Let {{{ a }}} = grams of 75% gold needed
Let {{{ b }}} = grams of 50% gold needed
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(1) {{{ a + b = 300 }}}
(2) {{{ ( .75a + .5b ) / 300 = .58 }}}
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(2) {{{ .75a + .5b = .58*300 }}}
(2) {{{ .75a + .5b = 174 }}}
(2) {{{ 75a + 50b = 17400 }}}
Multiply both sides of (1) by {{{ 50 }}} and
subtract (1) from (2)
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(2) {{{ 75a + 50b = 17400 }}}
(1) {{{ -50a - 50b = -15000 }}}
{{{ 25a = 2400 }}}
{{{ a = 96 }}}
and, since
(1) {{{ a + b = 300 }}}
(1) {{{ b = 204 }}}
96 grams of 75% gold are needed
204 grams of 50% gold are needed
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check:
(2) {{{ ( .75*96 + .5*204 ) / 300 = .58 }}}
(2) {{{ ( 72 + 102 ) / 300 = .58 }}}
(2) {{{ 174 = .58*300 }}}
(2) {{{ 174 = 174 }}}
OK