Question 1155684
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The method shown by tutor @josgarithmetic is the fastest and easiest way to solve a two-part mixture problem like this.<br>
If the numbers in the problem are "nice", a solution by this method can be obtained in a small fraction of the time required for a formal algebraic solution.<br>
In this problem, the numbers ARE nice; being good at mental arithmetic, I solved the problem within a couple of seconds after reading it.<br>
I find her explanation of the method difficult to understand, so here I am showing two different ways to understand the method.<br>
(1) 4% is "twice as close" to 3% as it is to 6%; therefore the mixture should use twice as much 3% as it does 6%.<br>
...or...<br>
(2) 4% is 1/3 of the way from 3% to 6%; therefore 1/3 of the mixture should be the 6%.<br>
Either way of thinking leads quickly to the answer of 30 quarts of the 3% butterfat milk and 15 quarts of the 6% butterfat milk.<br>