Question 855231
Let {{{ a }}} = ml of 23% solution needed
Let {{{ b }}} = ml of 57% solution needed
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(1) {{{ a + b = 34 }}}
(2) {{{ ( .23a + .57b ) / 34 = .32 }}}
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(2) {{{ .23a + .57b = .32*34 }}}
(2) {{{ .23a + .57b = 10.88 }}}
(2) {{{ 23a + 57b = 1088 }}}
Multiply both sides of (1) by {{{ 23 }}}
and subtract (1) from (2)
(2) {{{ 23a + 57b = 1088 }}}
(1) {{{ -23a - 23b = -782 }}}
{{{ 34b = 306 }}}
{{{ b = 9 }}}
and
(1) {{{ a + b = 34 }}}
(1) {{{ a = 34 - 9 }}}
(1) {{{ a = 25 }}}
25 ml of 23% solution is needed
9 ml of 57% solution is needed
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check:
(2) {{{ ( .23*25 + .57*9 ) / 34 = .32 }}}
(2) {{{ 5.75 + 5.13 = .32*34 }}}
(2) {{{ 10.88 = 10.88 }}}
OK