Question 720623
Let {{{ a }}} = liters of 5% solution needed
Let {{{ b }}} = liters of 20% solution needed
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(1) {{{ a + b = 30 }}}
(2) {{{ ( .05a + .2b ) / 30 = .1 }}}
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(2) {{{ .05a + .2b = 3 }}}
(2) {{{ 5a + 20b = 300 }}}
Multiply both sides of (1) by {{{ 5 }}} and
subtract (1) from (2)
(2) {{{ 5a + 20b = 300 }}}
(1) {{{ -5a - 5b = -150 }}}
{{{ 15b = 150 }}}
{{{ b = 10 }}}
and, since
(1) {{{ a + b = 30 }}}
(1) {{{ a = 20 }}}
20 liters of 5% solution are needed
10 liters of 20% solution are needed
check answer:
(2) {{{ ( .05*20 + .2*10 ) / 30 = .1 }}}
(2) {{{ ( 1+ 2 ) / 30 = .1 }}}
(2) {{{ 3/30 = .1 }}}
(2) {{{ 3 = 3 }}}
OK