A certain smoothie A is three-fifths blueberries and 40%

Question

A certain smoothie A is three-fifths blueberries and 40% raspberries by weight. Another smoothie B is three-quarters banana and one-quarter raspberries by weight. If the mixed smoothie of A and B is 30% raspberries by weight, how much weight of this mixture belongs to smoothie A?

(A) 10%
(B) 33.33%
(C) 45%
(D) 50%
(E) 66.66%

(A) 10%
(B) 33.33%
(C) 45%
(D) 50%
(E) 66.66%

Hiho · Answer

The way I did it was by putting weights on the smoothies to reach the ammount of raspberry in the mixed smoothie.

Like this:
0.4*a+(1-a)*0.25=0.3

Where 0.4 is the percent of the raspberry in a, and 0.25 is the percent of the raspberry in b. A is the (so far) unknown ammount of smoothie A in the complete smoothie which has 0.3 percent raspberry. (1-a) is basically b, because adding the ammount of A and B makes a total of 100%(1).

By solving the equation you'll reach

0.15a=0.05
a=0.3333

I'm not sure if there's a better method, that's just the way I solved it.

I also apologize in advance if my explanation wasn't understandable. I am not used to writing math in text form yet.

Bunuel · Answer

A is 40% raspberries;
B is 25% raspberries.
A and B is 30% raspberries;

30% raspberries in the mixed smoothie of A and B come from 40% raspberries in A and 25% raspberries in B, thus:

0.3(A+B)=0.4A+0.25B --> 0.1A=0.05B --> A/B=1/2 --> A/(A+B)=1/3.

Answer: B.

fozzzy · Answer

I understood everything except that step in red.

Bunuel · Answer

A/B=1/2 --> 2A=B --> A/(A+B)=A/(A+2A)=1/3.

Hiho · Answer

The question was how much A is of the entire smoothie. To get there you divide A by the total batch. A+B = total A/(A+B) = Percentage of A in the total batch.

PareshGmat · Answer

I solved this using alligation method as follows:

So, total = 15, contribution from A = 5; So 5/15 * 100 = 33.33 % 
Answer = B

EMPOWERgmatRichC · Answer

HI All,

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%

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

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A certain smoothie A is three-fifths blueberries and 40%

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