Question 529845
Let {{{a}}} = liters of 1% solution needed
Let {{{b}}} = liters of 9% solution needed
given:
(1) {{{ a + b = 5 }}} liters
(2) {{{ (.01a + .09b) / 5 = .0324 }}}
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(2) {{{ (.01a + .09b) / 5 = .0324 }}}
(2) {{{ (.01a + .09b)  = .0324*5 }}}
(2) {{{ .01a + .09b = .162 }}}
(2) {{{ a + 9b = 16.2 }}}
Subtract (1) from (2)
(2) {{{ a + 9b = 16.2 }}}
(1) {{{ -a - b = -5 }}}
{{{ 8b = 11.2 }}}
{{{ b = 1.4 }}}
and, since
(1) {{{ a + b = 5 }}}
(1) {{{ a + 1.4 = 5 }}}
(1) {{{ a = 3.6 }}}
3.6 liters of 1% solution are needed
1.4 liters of 9% solution are needed
check:
(2) {{{ (.01*3.6 + .09*1.4) / 5 = .0324 }}}
(2) {{{ ( .036 + .126 ) / 5 = .0324 }}}
(2) {{{ .162 = 5*.0324 }}}
(2) {{{ .162 = .162 }}}
OK