Question 490730
Let {{{a}}} = liters of 10% solution needed
Let {{{b}}} = liters of 60% solution needed
given:
(1) {{{ a + b = 50 }}}
(2) {{{ ( .1a + .6b) / 50 = .4 }}}
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(2) {{{ .1a + .6b = 20 }}}
(2) {{{ a + 6b = 200 }}}
Subtract (1) from (2)
(2) {{{ a + 6b = 200 }}}
(1) {{{ -a - b = -50 }}}
{{{ 5b = 150 }}}
{{{ b = 30 }}}
and, since
(1) {{{ a + b = 50 }}}
(1) {{{ a + 30 = 50 }}}
(1) {{{ a = 20 }}}
20 liters of 10% solution and 30
liters of 60% solution are needed
check:
(2) {{{ ( .1a + .6b) / 50 = .4 }}}
(2) {{{ ( .1*20 + .6*30) / 50 = .4 }}}
(2) {{{ ( 2 + 18) / 50 = .4 }}}
(2) {{{ 20/50 = .4 }}}
(2) {{{ 20 = 20 }}}
OK