Question 515871
Let {{{ a }}} = ml of 95% alcohol needed
Let {{{ b }}} = ml of water needed
given:
(1) {{{ a + b =200 }}} ml
(2) {{{ .95a / ( a + b ) = .35 }}}
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(2) {{{ .95a  = .35*(a + b) }}}
(2) {{{ .95a = .35a + .35b }}}
(2) {{{ .6a = .35b }}}
(2) {{{ 60a = 35b }}}
(2) {{{ 12a = 7b }}}
and,
(1) {{{ a = 200 - b }}}
By substitution:
(2) {{{ 12*( 200 - b ) = 7b }}}
(2) {{{ 2400 - 12b = 7b }}}
(2) {{{ 19b = 2400 }}}
(2) {{{ b = 126.32 }}}
and
(1) {{{ a = 200 - b }}}
(1) {{{ a = 200 - 126.32 }}}
(1) {{{ a = 73.68 }}}
74 ml of 95% alcohol are needed
126 ml of water are needed
check answer:
(2) {{{ .95a / ( a + b ) = .35 }}}
(2) {{{ .95*74 / 200 = .35 }}}
(2) {{{ 70.3 / 200 = .35 }}}
(2) {{{ 70.3 = 70 }}}
close enough