<PRE><B>Question 1142452</B>
&lt;br&gt;
The standard algebraic approach for mixture problems like this would be something like this:&lt;br&gt;
x cc of 30% alcohol, plus (30-x) cc of 45% alcohol, yields 30 cc of 39% alcohol:&lt;br&gt;
{{{.30(x)+.45(30-x) = .39(30)}}}&lt;br&gt;
You can solve that using basic algebra.&lt;br&gt;
That method gives good practice with algebra; you should understand why and how it works.&lt;br&gt;
But mixture problems like this can be solved much faster informally, with only logical reasoning and basic arithmetic.&lt;br&gt;
Here is the solution using this alternate method.&lt;br&gt;
(1) 39% is 3/5 of the way from 30% to 45%.  (Easy to determine if you are good with mental math; otherwise, picturing the three percentages on a number line might help.)&lt;br&gt;
(2) That means 3/5 of the mixture must be the 45% alcohol.&lt;br&gt;
So...&lt;br&gt;
ANSWER: 3/5 of 30 cc = 18cc of 45% alcohol; the rest, 12cc, of 30% alcohol.</PRE>