Question 562256
given:
(1) {{{ a + b + c = 20 }}}
{{{ .38*20 = 7.6 }}} liters of acid in mixture
(2) {{{ .3a + .2b + .6c = 7.6 }}}
(3) {{{ c/a = 2/1 }}}
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(3) {{{ c = 2a }}}
(2) {{{ 3a + 2b + 6c = 76 }}}
Multiply both sides of (1) by {{{ 2 }}}
and subtract (1) from (2)
(2) {{{ 3a + 2b + 6c = 76 }}}
(1) {{{ -2a - 2b - 2c = 40 }}}
{{{ a + 4c = 36 }}}
Substitute (3) into this
{{{ a + 4*2a  = 36 }}}
{{{ 9a = 36 }}}
{{{ a = 4 }}}
and
(3) {{{ c = 2a }}}
(3) {{{ c = 2*4 }}}
(3) {{{ c = 8 }}}
(1) {{{ a + b + c = 20 }}}
(1) {{{ 4 + b + 8 = 20 }}}
(1) {{{ b = 20 - 12 }}}
(1) {{{ b = 8 }}}
4 liters of A
8 liters of B
8 liters of C are needed
check:
(2) {{{ .3a + .2b + .6c = 7.6 }}}
(2) {{{ 1.2 + 1.6 + 4.8  = 7.6 }}}
(2) {{{ 7.6 = 7.6 }}}
OK
(1) {{{ a + b + c = 20 }}}
(1) {{{ 4 + 8 + 8 = 20 }}}
(1) {{{ 20 = 20 }}}
OK