Question 845168
Let {{{ a }}} = kg of 50% silver needed
Let {{{ b }}} = kg of 20% silver needed
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(1) {{{ a + b = 100 }}}
(2) {{{ ( .5a + .2b ) / 100 = .45 }}}
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(2) {{{ .5a + .2b = 45 }}}
(2) {{{ 5a + 2b = 450 }}}
Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 5a + 2b = 450 }}}
(1) {{{ -2a - 2b = -200 }}}
{{{ 3a = 250 }}}
{{{ a = 83.333 }}}
and
(1) {{{ a + b = 100 }}}
(1) {{{ b = 100 - 83.333 }}}
(1) {{{ b = 16.667 }}}
83.333 kg of 50% silver is needed
16.667 kg of 20% silver is needed 
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check:
(2) {{{ ( .5a + .2b ) / 100 = .45 }}}
(2) {{{ ( .5*83.333 + .2*16.667 ) / 100 = .45 }}}
(2) {{{ ( 41.6665 + 3.3334 ) / 100 = .45 }}}
(2) {{{ 45.00005 = 45 }}}
close enough