Question 1118534
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Tutor @ikleyn has shown a solution using the usual algebraic method; she has also pointed you towards several other examples of similar problems which use the same method.<br>
It is of course useful to know that method.  However, there is a much faster and easier way to find the answer to ANY mixture problem like this where two "ingredients" are being mixed.<br>
For your problem, here is the entire set of calculations required:<br>
(1) 50-30 = 20; 30-20 = 10
(2) 20:10 = 2:1
(3) 2 parts 30% acid to 1 part 50% acid
(4) 2/3 of 120 ounces = 80 ounces of 30% acid; 1/3 of 120 ounces = 40 ounces of 50% acid<br>
It's even faster if you think in terms of what those calculations mean.  Here is the way I think of it:<br>
"The 30% target is twice as close to 20% as it is to 50% (step (1) above); therefore the solution must use twice as much of the 20% ingredient as the 50% ingredient (step (2) above).  A 2:1 ratio with a total of 120 ounces means 80 ounces of 20% and 40 ounces of 50% (steps 3 and 4 above)."