Question 495507
Let {{{a}}} = liters of solution A needed
Let {{{b}}} = liters of solution B needed
given:
(1) {{{ a + b = 20 }}}
(2) {{{ .5a + .2b = .32*20 }}}
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(2) {{{ .5a + .2b = 6.4 }}}
(2) {{{ 5a + 2b = 64 }}}
Multiply both sides of (1) by {{{2}}}
and subtract (1) from (2)
(2) {{{ 5a + 2b = 64 }}}
(1) {{{ -2a - 2b = -40 }}}
{{{ 3a = 24 }}}
{{{ a = 8 }}}
and, since,
(1) {{{ a + b = 20 }}}
(1) {{{ b = 20 - 8 }}}
(1) {{{ b = 12 }}}
8 liters of solution A are needed
12 liters of solution B are needed
check answer:
(2) {{{ .5a + .2b = 6.4 }}}
(2) {{{ .5*8 + .2*12 = 6.4 }}}
(2) {{{ 4 + 2.4 = 6.4 }}}
(2) {{{ 6.4 = 6.4 }}}
OK