Question 855796
Let {{{ a }}} = pounds of 70% alloy needed
Let {{{ b }}} = pounds of 90% alloy needed
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(1) {{{ a + b = 100 }}}
(2) {{{ ( .7a + .9b ) / 100 = .81 }}}
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(2) {{{ .7a + .9b = 81 }}}
(2) {{{ 7a + 9b = 810 }}}
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Multiply both sides of (1) by {{{ 7 }}}
and subtract (1) from (2)
(2) {{{ 7a + 9b = 810 }}}
(1) {{{ -7a - 7b = -700 }}}
{{{ 2b = 110 }}}
{{{ b = 55 }}}
and
(1) {{{ a + b = 100 }}}
{{{ a = 45 }}}
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45 pounds of 70% alloy are needed
55 pounds of 90% alloy are needed
check:
(2) {{{ ( .7*45 + .9*55 ) / 100 = .81 }}}
(2) {{{ ( 31.5 + 49.5 ) / 100 = .81 }}}
(2) {{{ 81 = .81*100 }}}
(2) {{{ 81 = 81 }}}
OK