Question 1157201
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Here is a non-standard, non-algebraic method for solving any two-part mixture problem like this.<br>
You are starting with 2L of 100% grape juice; you are adding some 40% fruit juice to get a mixture that is 64% fruit juice.<br>
Imagine the three percentages on a number line: 100, 64, and 40.  Imagine "walking" along the number line, starting from 100 and moving toward 40, stopping when you get to 64.  What fraction of the distance have you gone?<br>
100 to 40 is 60; 100 to 64 is 36.  You have gone 36/60 = 3/5 of the distance.<br>
That means 3/5 of the mixture has to be the 40% fruit juice that you are adding to the original 100% grape juice.<br>
So 2/5 of the mixture is the original 2L of grape juice; that means the 3/5 of the mixture is 3L.<br>
ANSWER:
Add 3L of fruit juice to get a mixture that is 64% fruit juice.<br>
CHECK:
1.00(2)+.40(3) = 2+1.2 = 3.2
.64(2+3) = .64(5) = 3.2<br>