Question 1086591
Let {{{ a }}} = liters of the 18% mixture needed
Let {{{ b }}} = liters of the 50% mixture needed
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(1) {{{ a + b = 2 }}}
(2) {{{ ( .18a + .5b ) / 2 = .26 }}}
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(2) {{{ .18a + .5b = .52 }}}
(2) {{{ 18a + 50b = 52 }}}
(2) {{{ 9a + 25b = 26 }}}
Multiply both sides of (1) by {{{ 9 }}} and
subtract (1) from (2)
(2) {{{ 9a + 25b = 26 }}}
(1) {{{ -9a - 9b = -18 }}}
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{{{ 16b = 8 }}}
{{{ b = .5 }}}
and
(1) {{{ a + b = 2 }}}
(1) {{{ a + .5 = 2 }}}
(1) {{{ a = 1.5 }}}
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1.5 liters of the 18% mixture are needed
.5 liters of the 50% mixture is needed
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check:
(2) {{{ ( .18a + .5b ) / 2 = .26 }}}
(2) {{{ ( .18*1.5 + .5*.5 ) / 2 = .26 }}}
(2) {{{ ( .27 + .25 ) / 2 = .26 }}}
(2) {{{ .52 = .26*2 }}}
(2) {{{ .52 = .52 }}}
OK