Question 696425
Let {{{ a }}} = ml of 10% solution
Let {{{ b }}} = ml of 15% alcohol
given:
(1) {{{ a + b = 100 }}}
(2) {{{ ( .1a + .15b ) / 100 = .12 }}}
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(2) {{{ .1a + .15b = .12*100 }}}
(2) {{{ .1a + .15b = 12 }}}
(2) {{{ 10a + 15b = 1200 }}}
Multiply both sides of (1) by {{{ 10 }}}
and subtract (1) from (2)
(2) {{{ 10a + 15b = 1200 }}}
(1) {{{ -10a - 10b = -1000 }}}
{{{ 5b = 200 }}}
{{{ b = 40 }}}
and, since
(1) {{{ a + b = 100 }}}
(1) {{{ a = 100 - b }}}
(1) {{{ a = 100 - 40 }}}
(1) {{{ a = 60 }}}
60 ml of 10% solution is needed
40 ml of 15% alcohol is needed
check:
(2) {{{ ( .1a + .15b ) / 100 = .12 }}}
(2) {{{ ( .1*60 + .15*40 ) / 100 = .12 }}}
(2) {{{ ( 6 + 6 ) / 100 = .12 }}}
(2) {{{ 12 = .12*100 }}}
(2) {{{ 12 = 12 }}}
OK