Question 1152731
Let {{{ a }}} = pounds of 55% mix needed
Let {{{ b }}} = pounds of 25% mix needed
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(1) {{{ a + b = 1200 }}}
(2) {{{ ( .55a + .25b ) / 1200 = .45 }}}
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(2) {{{ .55a + .25b = 540 }}}
(2) {{{ 55a + 25b = 54000 }}}
(2) {{{ 11a + 5b = 10800 }}}
Multiply both sides of (1) by {{{ 5 }}} 
and subtract (1) from (2)
(2) {{{ 11a + 5b = 10800 }}}
(2) {{{ -5a - 5b = -6000 }}}
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{{{ 6a = 4800 }}}
{{{ a = 800 }}}
and
(1) {{{ a + b = 1200 }}}
(1) {{{ 800 + b = 1200 }}}
(1) {{{ b = 400 }}}
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800 pounds of 55% mix are needed
400 pounds of 25% mix are needed
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check:
(2) {{{ ( .55a + .25b ) / 1200 = .45 }}}
(2) {{{ ( .55*800 + .25*400 ) / 1200 = .45 }}}
(2) {{{ ( 440 + 100 ) / 1200 = .45 }}}
(2) {{{ 540 = .45*1200 }}}
(2) {{{ 540 = 540 }}}
OK