A certain smoothie A is three-fifths blueberries and 40% : GMAT Problem Solving (PS)
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# A certain smoothie A is three-fifths blueberries and 40%

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A certain smoothie A is three-fifths blueberries and 40% [#permalink]

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21 Dec 2012, 22:50
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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%
[Reveal] Spoiler: OA

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Re: A certain smoothie A is three-fifths blueberries and 40% [#permalink]

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22 Dec 2012, 03:25
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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.
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Re: A certain smoothie A is three-fifths blueberries and 40% [#permalink]

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22 Dec 2012, 03:51
fozzzy wrote:
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 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.

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Re: A certain smoothie A is three-fifths blueberries and 40% [#permalink]

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22 Dec 2012, 04:05
Bunuel wrote:
fozzzy wrote:
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 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.

I understood everything except that step in red.
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Re: A certain smoothie A is three-fifths blueberries and 40% [#permalink]

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22 Dec 2012, 04:13
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Expert's post
fozzzy wrote:
Bunuel wrote:
fozzzy wrote:
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 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.

I understood everything except that step in red.

A/B=1/2 --> 2A=B --> A/(A+B)=A/(A+2A)=1/3.
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Re: A certain smoothie A is three-fifths blueberries and 40% [#permalink]

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22 Dec 2012, 04:14
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fozzzy wrote:
Bunuel wrote:
fozzzy wrote:
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 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.

I understood everything except that step in red.

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.
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Re: A certain smoothie A is three-fifths blueberries and 40% [#permalink]

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27 Jun 2013, 02:10
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I solved this using alligation method as follows:

So, total = 15, contribution from A = 5; So 5/15 * 100 = 33.33 %
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Re: A certain smoothie A is three-fifths blueberries and 40% [#permalink]

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24 Dec 2014, 05:47
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Re: A certain smoothie A is three-fifths blueberries and 40% [#permalink]

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24 Dec 2014, 08:26
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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%

[Reveal] Spoiler:
B

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Re: A certain smoothie A is three-fifths blueberries and 40% [#permalink]

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26 Feb 2016, 06:42
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A certain smoothie A is three-fifths blueberries and 40%   [#permalink] 26 Feb 2016, 06:42
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