Question 1126661
Let {{{ a }}} = pounds of 18% silver needed
Let {{{ b }}} = pounds of 73% silver needed
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(1) {{{ a + b = 10 }}}
(2) {{{ ( .18a + .73b ) / 10 = .33 }}}
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(2) {{{ .18a + .73b = 3.3 }}}
(2) {{{ 18a + 73b = 330 }}}
Multiply both sides of (1) by {{{ 18 }}}
and subtract (1) from (2)
(2) {{{ 18a + 73b = 330 }}}
(1) {{{ -18a - 18b = -180 }}}
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{{{ 55b = 150 }}}
{{{ b = 2.727 }}}
and
{{{ a + 2.727 = 10 }}}
{{{ a = 7.273 }}}
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7.273 pounds of 18% silver
2.727 pounds of 73% silver
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check:
(2) {{{ ( .18a + .73b ) / 10 = .33 }}}
(2) {{{ ( .18*7.273 + .73*2.727 ) / 10 = .33 }}}
(2) {{{ ( 1.309 + 1.991 ) / 10 = .33 }}}
(2) {{{ 3.299 = 3.3 }}}
error due to rounding off