Question 1178938
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(1) Certainly memorizing a magic formula as shown by tutor @josgarithmetic is not a good way to LEARN HOW to work problems like this.<br>
(2) Formal algebraic solutions as shown by the other tutors -- in which it is clear WHY the method works -- are of course fine.<br>
(3) And if a formal algebraic solution is not required, here is what is almost certainly the fastest and easiest path to the answer.<br>
Consider, perhaps using a number line, that the 50% of the mixture is 2/3 of the way from 40% to 55%, the percentages of the two ingredients.
That means 2/3 of the mixture must be the 55% ingredient.<br>
So the 2L of the 40% juice is 1/3 of the mixture; that means the 2/3 of the mixture that is the 55% juice is 4L.<br>
ANSWER: 4L of 55% juice.<br>
CHECK:
.4(2)+.55(4) = .8+2.2 = 3
.5(6) = 3<br>