Question 1062868
Let {{{ a }}} = liters of 25% OJ needed
Let {{{ b }}} = liters of 5% OJ needed
{{{ .25a }}} = liters of OJ in the 25% juice
{{{ .05b }}} = liters of OJ in the 5% juice
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(1) {{{ a + b = 20 }}}
(2) {{{ ( .25a + .05b ) / 20 = .1 }}}
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(2) {{{ .25a + .05b = 2 }}}
(2) {{{ 25a + 5b = 200 }}}
(2) {{{ 5a + b = 40 }}}
Subtract (1) from (2)
(2) {{{ 5a + b = 40 }}}
(1) {{{ -a - b = -20 }}}
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{{{ 4a = 20 }}}
{{{ a = 5 }}}
and
(1) {{{ a + b = 20 }}}
(1) {{{ 5 + b = 20 }}}
(1) {{{ b = 15 }}}
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5 liters of 25% OJ is needed
15 liters of 5% OJ is needed
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check:
(2) {{{ ( .25a + .05b ) / 20 = .1 }}}
(2) {{{ ( .25*5 + .05*15 ) / 20 = .1 }}}
(2) {{{ ( 1.25 + .75 ) / 20 = .1 }}}
(2) {{{ 2 = .1*20 }}}
(2) {{{ 2 = 2 }}}
OK