Question 497608
Let {{{a}}} = ounces of 16% hydrochloric acid solution needed
Let {{{b}}} = ounces of 8% hydrochloric acid solution needed
given:
(1) {{{ a + b = 32 }}}
(2) {{{ .16a + .08b = .12*32 }}}
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(2) {{{ .16a + .08b = 3.84 }}}
Multiply both sides of (2) by {{{100}}}
(2) {{{ 16a + 8b = 384 }}}
Multiply both sides of (1) by {{{8}}}
and subtract (1) from (2)
(2) {{{ 16a + 8b = 384 }}}
(1) {{{-8 a - 8b = 256 }}}
{{{ 8a = 128 }}}
{{{ a = 16 }}}
and, since
(1) {{{ a + b = 32 }}}
(1) {{{ b = 16 }}}
16 ounces of 16% hydrochloric acid solution are needed
16 ounces of 8% hydrochloric acid solution are needed
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check answer:
(2) {{{ .16*16 + .08*16 = 3.84 }}}
(2) {{{ 2.56 + 1.28 = 3.84 }}}
(2) {{{ 3.84 = 3.84 }}}
OK