Question 292646
In words:
(total quarts of soap)/(total quarts of solution) = 50%
Let {{{a}}} = quarts of 30% solution
Let {{{b}}} = quarts of 60% solution
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given:
{{{a + b = 60}}}
{{{b = 60 - a}}}
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{{{(.3a + .6b)/60 = .5}}}
{{{.3a + .6b = 30}}}
{{{3a + 6b = 300}}}
{{{a + 2b = 100}}}
By substitution:
{{{a + 2*(60 - a) = 100}}}
{{{a + 120 - 2a = 100}}}
{{{-a = -20}}}
{{{a = 20}}}
and, since
{{{a + b = 60}}}
{{{b = 60 - 20}}}
{{{b = 40}}}
20 quarts of 30% solution and 40 quarts of 60% solution are needed
check:
{{{(.3a + .6b)/60 = .5}}}
{{{(.3*20 + .6*40)/60 = .5}}}
{{{(6 + 24)/60 = .5}}}
{{{30/60 = .5}}}
{{{.5 = .5}}}
OK