Question 940860
Let {{{a }}} = grams of 25% alloy needed
Let {{{ b }}} = grams of 50% alloy needed
{{{ .25a }}} = grams of copper in 25% alloy
{{{ .5b }}} = grams of copper in 50% alloy
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(1) {{{ a +b = 1000 }}}
(2) {{{ ( .25a + .5b ) / 1000 = .45 }}}
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(2) {{{ .25a + .5b = 450 }}}
(2) {{{ 25a + 50b = 45000 }}}
Multiply both sides of (1) by {{{ 25 }}}
and subtract (1) from (2)
(2) {{{ 25a + 50b = 45000 }}}
(1) {{{ -25a - 25b  = -25000 }}}
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{{{ 25b = 20000 }}}
{{{ b = 800 }}}
and, since
(1) {{{ a +b = 1000 }}}
(1) {{{ a = 200 }}}
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200 grams of 25% alloy are needed
800 grams of 50% alloy are needed
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check:
(2) {{{ ( .25*200 + .5*800 ) / 1000 = .45 }}}
(2) {{{ ( 50 + 400 ) / 1000 = .45 }}}
(2) {{{ 450 = .45*1000 }}}
(2) {{{ 450 = 450 }}}
OK