In these sorts of scenarios, when you're not given a specific amount of the items involved (in this case, Smoothie A and Smoothie B), you can TEST VALUES and use real numbers to answer the question.
Here, we know:
Smoothie A is 40% raspberries
Smoothie B is 25% raspberries
We want to mix some of each and end up with a 30% raspberry mixture
Here's how to TEST VALUES:
Lets's say we have 10oz. of Smoothie A...
10(40%) = 4 oz. raspberries
Now, we can calculate how much Smoothie B we need by using the Weighted Average Formula:
Let's say we have Xoz. of Smoothie B...
X(25%) = .25X oz. raspberries
Rasp/All = (4+.25X)/(10+X) = .3
4+.25X = 3 + .3X
1 = .05X
20 = X
This means that we would need 20 ounces of Smoothie B to be mixed with 10 ounces of Smoothie A to end up with a 30% raspberry mix at the end. The question asks what percent of the mixture "belongs to Smoothie A"
A/All = 10/30 = 1/3 = 33.33%
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