Question 1160519
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Here is an informal method for solving mixture problems like this that will get you to an answer much faster and with less effort than an algebraic method.<br>
You are starting with water at 78 degrees; you are adding water at 90 degrees, until the mixture reaches 80 degrees.<br>
80 degrees is 1/6 of the way from 78 degrees to 90 degrees.  (78 to 90 is 12; 78 to 80 is 2; 2/12 = 1/6).<br>
That means 1/6 of the final mixture is what you are adding.<br>
So the 30,000 gallons originally in the pool is 5/6 of the final mixture; that means 1/6 of the final mixture -- the 90 degree water you are adding -- is 30,000/5 = 6,000 gallons.<br>
ANSWER: 6000 gallons of 90 degree water<br>