Question 1129873
Let {{{ a }}} = liters of 25% solution needed
Let {{{ b }}} = liters of 55% solution needed
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(1) {{{ a + b = 465 }}}
(2) {{{ ( .25a + .55b ) / 465  = .45 }}}
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(2) {{{ .25a + .55b = 209.25 }}}
(2) {{{ 25a + 55b = 20925 }}}
(2) {{{ 5a + 11b = 4185 }}}
Multiply both sides of (1) by {{{ 5 }}} and subtract (1) from (2)
(1) {{{ -5a - 5b = -2325 }}}
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{{{ 6b = 1860 }}}
{{{ b = 310 }}}
and
(1) {{{ a + 310 = 465 }}}
(1) {{{ a = 155 }}}
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155 liters of 25% mixture
310 liters of 55% mixture
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check:
(2) {{{ ( .25a + .55b ) / 465  = .45 }}}
(2) {{{ ( .25*155 + .55*310 ) / 465  = .45 }}}
(2) {{{ ( 38.75 + 170.5 )/465 = .45 }}}
(2) {{{ ( 209.25 ) / 465 = .45 }}}
(2) {{{ 209.25 = .45*465 }}}
(2) {{{ 209.25 = 209.25 }}}
OKJ