Question 751374
Let {{{ a }}} = liters of 50% lemonade needed
Let {{{ b }}} = liters of 25% lemonade needed
{{{ .5a }}} = liters of lemon juice in 50% lemonade
{{{ .25b }}} = liters of lemon juice in 25% lemonade
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(1) {{{ a + b = 10 }}}
(2) {{{ ( .5a + .25b ) / 10 = .35 }}}
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(2) {{{ .5a + .25b = 3.5 }}}
(2) {{{ 50a + 25b = 350 }}}
(2) {{{ 2a + b = 14 }}}
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Subtract (1) from (2)
(2) {{{ 2a + b = 14 }}}
(1) {{{ -a - b = -10 }}}
{{{ a = 4 }}}
and, since
(1) {{{ a + b = 10 }}}
(1) {{{ b = 6 }}}
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6 liters of 25% lemonade is needed
check:
(2) {{{ ( .5*4 + .25*6 ) / 10 = .35 }}}
(2) {{{ ( 2 + 1.5 ) / 10 = .35 }}}
(2) {{{ 3.5 = .35*10 }}}
(2) {{{ 3.5 = 3.5 }}}
OK