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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] New post 21 Dec 2012, 23:50
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70% (01:56) correct 29% (01:07) wrong based on 2 sessions
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] New post 22 Dec 2012, 04:25
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] New post 22 Dec 2012, 04:51
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.

Answer: B.
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Re: A certain smoothie A is three-fifths blueberries and 40% [#permalink] New post 22 Dec 2012, 05:05
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.

Answer: B.


I understood everything except that step in red.
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Re: A certain smoothie A is three-fifths blueberries and 40% [#permalink] New post 22 Dec 2012, 05:13
1
This post received
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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.

Answer: B.


I understood everything except that step in red.


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

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!


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Re: A certain smoothie A is three-fifths blueberries and 40% [#permalink] New post 22 Dec 2012, 05:14
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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.

Answer: B.


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. :)
Re: A certain smoothie A is three-fifths blueberries and 40%   [#permalink] 22 Dec 2012, 05:14
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