<PRE><B>Question 1103821</B>
&lt;br&gt;
Here is a method for solving mixture problems like this that is much faster and easier then the standard algebraic method usually shown.&lt;br&gt;
The method uses a diagram like this:&lt;br&gt;
{{{matrix(3,3,12,&quot;&quot;,3,&quot;&quot;,8,&quot;&quot;,5,&quot;&quot;,4)}}}&lt;br&gt;
The 12 and 5 in the first column are the percentages of the two ingredients.
The 8 in the middle column is the percentage of the mixture.
The 3 and 4 in the last column are the differences, computed diagonally, between the numbers in the first and second columns: 12-8=4; 8-5=3.&lt;br&gt;
When the numbers given in the problem are used in this way, the numbers in the last column give the ratio in which the two ingredients need to be mixed.&lt;br&gt;
In this problem, those numbers tell us that the 12% ingredient and the 5% ingredient need to be mixed in the ratio 3:4 to make an 8% mixture.&lt;br&gt;
A ratio of 3:4 means 3/7 of the mixture should be the 12% solution and 4/7 should be the 5% solution.  So
12%: 4/7 of 63 gallons = 36 gallons
5%: 3/7 of 63 gallons = 27 gallons</PRE>