Question 588182
Let {{{ a }}} = ounces of 10% solution needed
Let {{{ b }}} = ounces of 15% solution needed
{{{ .1a }}} = ounces of acid in 10% solution
{{{ .15b }}} = ounces of acid in 15% solution
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(1) {{{ a + b =  20 }}}
(2) {{{ ( .1a + .15b ) / 20 = .12 }}}
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(2) {{{ .1a + .15b = .12*20 }}}
(2) {{{ .1a + .15b = 2.4 }}}
(2) {{{ 10a + 15b = 240 }}}
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Multiply both sides of (1) by {{{ 10 }}}
and subtract (1) from (2)
(2) {{{ 10a + 15b = 240 }}}
(1) {{{ -10a - 10b = -200 }}}
{{{ 5b = 40 }}}
{{{ b = 8 }}}
and, since
{{{ a + b = 20 }}}
{{{ a + 8 = 20 }}}
{{{ a = 12 }}}
12 ounces of 10% solution is needed
8 ounces of 15% solution is needed
check:
(2) {{{ ( .1a + .15b ) / 20 = .12 }}}
(2) {{{ ( .1*12 + .15*8 ) / 20 = .12 }}}
(2) {{{ ( 1.2 + 1.2 ) / 20 = .12 }}}
(2) {{{ 2.4 / 20 = .12 }}}
(2) {{{ 2.4 = 2.4 }}}
OK