<PRE><B>Question 1161919</B>
&lt;br&gt;
&quot;Write your answer in complete sentences. Show all work.&quot;&lt;br&gt;
There is no sense in writing that in your post; that is your job, not ours.  We only show you how to solve the problem -- or how to set it up to be solved.&lt;br&gt;
(1) With formal algebra....&lt;br&gt;
70% of the 15 gallons you start with, plus 20% of the x gallons you are adding, equals 35% of the (x+15) gallons of the final mixture:&lt;br&gt;
{{{.70(15)+.20(x) = .35(15+x)}}}&lt;br&gt;
Solve using basic algebra, although the numbers are not particularly &quot;nice&quot;....&lt;br&gt;
(2) A completely different solution method, which will get you to the answer to any &quot;mixture&quot; problem like this much faster, and with far less effort, then the traditional formal algebraic method.&lt;br&gt;
You are starting with 70% solution and adding 20% solution, ending with 35% solution.&lt;br&gt;
Model that by thinking of walking along a number line from 70 to 20, stopping when you get to 35.&lt;br&gt;
What fraction of the distance have you gone when you stop? 70 to 20 is a distance of 50; 70 to 35 is a distance of 35.  You have gone 35/50 = 7/10 of the distance.&lt;br&gt;
That means 7/10 of the mixture is what you are adding.&lt;br&gt;
So the 15 gallons you started with is 3/10 of the final mixture; that means the 7/10 of the final mixture that you added is 35 gallons.&lt;br&gt;
ANSWER: 35 gallons&lt;br&gt;
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