Question 533457
Let {{{a}}} = ounces of 25% solution needed
Let {{{b}}} = ounces of 15% solution needed
given:
{{{ .25a }}} = ounces of acid in 25% solution
{{{ .15b }}} = ounces of acid in 15% solution
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given:
(1) {{{ a + b = 50 }}}
(2) {{{ ( .25a + .15b ) / 50 = .18 }}}
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(2) {{{ .25a + .15b = .18*50 }}}
(2) {{{ .25a + .15b = 9 }}}
(2) {{{ 25a + 15b = 900 }}}
(2) {{{ 5a + 3b = 180 }}}
Multiply both sides of (1) by {{{3}}}, and
subtract (1) from (2)
(2) {{{ 5a + 3b = 180 }}}
(1) {{{ -3a - 3b = -150 }}}
{{{ 2a = 30 }}}
{{{ a = 15 }}}
and, since
(1) {{{ a + b = 50 }}}
(1) {{{ 15 + b = 50 }}}
(1) {{{ b = 35 }}}
15 ounces of 25% solution are needed
35 ounces of 15% solution are needed
check:
(2) {{{ ( .25*15 + .15*35 ) / 50 = .18 }}}
(2) {{{ ( 3.75 + 5.25 ) / 50 = .18 }}}
(2) {{{ 9/50 = .18 }}}
(2) {{{ 9 = 9 }}}
OK