Question 263512
Let {{{a}}} = ml of 30% solution required
Let {{{b}}} = ml of 15% solution required
given:
She must end up with 150 ml, so
(1) {{{a + b = 150}}}
Amount of alcohol in 150 ml of 20% solution =
{{{.2*150 = 30}}} ml
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In words:
(alcohol in 30% solution) + (alcohol in 15% solution) = 
(alcohol in 20% solution)
{{{.3a + .15b = 30}}} 
Multiply both sides by {{{100}}}
(2) {{{30a + 15b = 3000}}}
Multiply both sides of (1) by {{{15}}} and
subtract from (2)
(2) {{{30a + 15b = 3000}}}
(1) {{{-15a - 15b = -2250}}}
{{{15a = 750}}}
{{{a = 50}}}
And, from (1),
{{{a + b = 150}}}
{{{50 + b = 150}}}
{{{b = 100}}}
50 ml of the 30% solution and 100 ml of the 15% solution
are required
check answer:
(2) {{{30a + 15b = 3000}}}
(2) {{{30*50 + 15*100 = 3000}}}
{{{1500 + 1500 = 3000}}}
{{{3000 = 3000}}}