Question 607400
Let {{{ a }}} = cc's of 6% solution
Let {{{ b }}} = cc's of 14% solution
{{{ .06a }}} = cc's of acid in 6% solution
{{{ .14b }}} = cc's of acid in 14% solution
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(1) {{{ a + b = 50 }}}
(2) {{{ ( .06a + .14b ) / 50 = .12 }}}
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(2) {{{ .06a + .14b = .12*50 }}}
(2) {{{ .06a + .14b = 6 }}}
(2) {{{ 6a + 14b = 600 }}}
Multiply both sides of (1) by {{{ 6 }}}
and subtract (1) from (2) 
(2) {{{ 6a + 14b = 600 }}}
(1) {{{ -6a - 6b = -300 }}}
{{{ 8b = 300 }}}
{{{ b = 37.5 }}}
and, since
(1) {{{ a + b = 50 }}}
(1) {{{ a + 37.5 = 50 }}}
(1) {{{ a = 12.5 }}}
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12.5 cc's of 6% solution are needed
37.5 cc's of 14% solution are needed
check:
(2) {{{ ( .06a + .14b ) / 50 = .12 }}}
(2) {{{ ( .06*12.5 + .14*37.5 ) / 50 = .12 }}}
(2) {{{ ( .75 + 5.25 ) / 50 = .12 }}}
(2) {{{ 6 / 50 = .12 }}}
(2) {{{ 6 = .12*50 }}}
(2) {{{ 6 = 6 }}}
OK