Question 991979
Let {{{ a }}} = pounds of 18% silver needed
Let {{{ b }}} = pounds of 80% silver needed
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(1) {{{ a + b = 3 }}}
(2) {{{ ( .18a + .8b ) / 3 = .43 }}}
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(2) {{{ .18a + .8b = 1.29 }}}
(2) {{{ 18a + 80b = 129 }}}
Multiply both sides of (1) by {{{ 18 }}}
and subtract (1) from (2)
(2) {{{ 18a + 80b = 129 }}}
(1) {{{ -18a - 18b = -54 }}}
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{{{ 62b = 75 }}}
{{{ b = 1.21}}}
and
(1) {{{ a + b = 3 }}}
(1) {{{ a = 1.79 }}}
1.79  pounds of 18% silver are needed
1.21 pounds of 80% silver are needed
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check:
(2) {{{ ( .18*1.79 + .8*1.21 ) / 3 = .43 }}}
(2) {{{ ( .3222 + .968 ) / 3 = .43 }}}
(2) {{{ 1.29 = 3*.43 }}}
(2) {{{ 1.29 = 1.29 }}}
OK