Question 373827
Let {{{a}}} = mg of the 1st liquid to be used
Let {{{b}}} = mg of the 2nd liquid to be used
given:
(1) {{{.2a + .4b = 40}}}
(2) {{{.3a + .2b = 30}}}
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Multiply both sides by {{{10}}}.
(1) {{{2a + 4b = 400}}}
(2) {{{3a + 2b = 300}}}
Multiply both sides of (2) by {{{2}}}
and subtract (1) from (2)
(2) {{{6a + 4b = 600}}}
(1) {{{-2a -4b = -400}}}
{{{4a = 200}}}
{{{a = 50}}}
and, since
(2) {{{3a + 2b = 300}}}
{{{150 + 2b = 300}}}
{{{2b = 150}}}
{{{b = 75}}}
50 mg of the 1st liquid and 75 mg of the 2nd liquid 
should be used