Question 958179
Let {{{ a }}} = ml of 9% HCL needed
Let {{{ b }}} = ml of 4% HCL needed
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(1) {{{ a + b = 50 }}} ml
(2) {{{ ( .09a + .04b ) / 50 = .06 }}}
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(2) {{{ .09a + .04b = .06*50 }}}
(2) {{{ .09a + .04b = 3 }}}
(2) {{{ 9a + 4b = 300 }}}
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Multiply both sides of (1) by {{{ 4 }}}
and subtract (1) from (2)
(2) {{{ 9a + 4b = 300 }}}
(1) {{{ -4a - -4b = -200 }}}
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{{{ 5a = 100 }}}
{{{ a = 20 }}}
and
(1) {{{ 20 + b = 50 }}}
(2) {{{ b = 30 }}}
20 ml of 9% HCL are needed
30 ml of 4% HCL are needed
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check:
(2) {{{ ( .09*20 + .04*30 ) / 50 = .06 }}}
(2) {{{ ( 1.8 + 1.2 ) / 50 = .06 }}}
(2) {{{ 3 = .06*50 }}}
(2) {{{ 3 = 3 }}}
OK