Question 559528
Let {{{ a }}} = ml of 2% alcohol needed
Let {{{ b }}} = ml of 18% alcohol needed
given:
{{{ .03*4000 = 120 }}} = ml of alcohol in 3% solution
(1) {{{ a + b = 4000 }}} ml
(2) {{{ .02a + .18b = 120 }}} ml
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(2) {{{ 2a + 18b = 12000 }}}
Multiply both sides of (1) by {{{2}}}
and subtract (1) from (2)
(2) {{{ 2a + 18b = 12000 }}}
(1) {{{ -2a - 2b = -8000 }}}
{{{ 16b = 4000 }}}
{{{ b = 250 }}}
and
(1) {{{ a + b = 4000 }}}
(1) {{{ a + 250 = 4000 }}}
(1) {{{ a = 4000 - 250 }}}
(1) {{{ a = 3750 }}}
3,750 ml of 2% alcohol and 250 ml of 
18% alcohol are needed
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check answer:
(2) {{{ .02a + .18b = 120 }}}
(2) {{{ .02*3750 + .18*250 = 120 }}}
(2) {{{ 75 + 45 = 120 }}}
(2) {{{ 120 = 120 }}}
OK