Question 715788
Let {{{ a }}} = grams of 50% alloy used
Let {{{ b }}} = grams of 70% alloy used
{{{ .5a }}} = grams of silver in 50% alloy
{{{ .7b }}} = grams of silver in 70% alloy 
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(1) {{{ ( .5a + .7b ) / 500 = .65 }}}
(2) {{{ a + b = 500 }}}
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(1) {{{ .5a + .7b = .65*500 }}}
(1) {{{ .5a + .7b = 325 }}}
(1) {{{ 5a + 7b = 3250 }}}
Multiply both sides of (2) by {{{ 5 }}}
and subtract from (1)
(1) {{{ 5a + 7b = 3250 }}}
(2) {{{ -5a - 5b = -2500 }}}
{{{ 2b = 750 }}}
{{{ b = 375 }}}
and, from (2)
(2) {{{ a + 375 = 500 }}}
(2) {{{ a = 125 }}}
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125 grams of 50% alloy was used
375 grams of 70% alloy was used
check:
(1) {{{ ( .5a + .7b ) / 500 = .65 }}}
(1) {{{ ( .5*125 + .7*375 ) / 500 = .65 }}}
(1) {{{ ( 62.5 + 262.5 ) / 500 = .65 }}}
(1) {{{ 325 / 500 = .65 }}}
(1) {{{ 325 = 325 }}}
OK