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505-555 (Easy)|   Mixture Problems|                     
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DanTheGMATMan
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A rabbit on a controlled diet is fed daily 300 grams of a 19 Jun 2024, 11:57
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­Classic mixture problem:

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Aboyhasnoname
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A rabbit on a controlled diet is fed daily 300 grams of a 13 Sep 2025, 05:18
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Reasoning of the question.
X and Y..If together equally..they will have 12.5% of protein......
12.5% means...12.5 grams out of 100 means out of 100 ..37.5 grams
We are just short of .5 grams.. So the actual amount should be nearby,....
Now it can't be 160...Because more of 160 means that less of Y ..so the protein will decrease in this case....
Means Y should be slightly higher....Answer B...

However...Clarity on it numerically....
Every 10 grams of mixture X adds 1 gram of protein X (lets just give the names for better understandin)
and Every 10 grams of mixture Y adds 1.5 grams of Protein Y...
Means when you remove 10 grams of X..You are removing 1 gram and then adding 1.5 grams.....for every 10 grams of X removed and Y added...
Since we are .5 short of 38 means we have to remove X by 10 gram and add Y by 10 gram..hence X is 140. B











tinman1412
A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10% protein and food Y contains 15% protein. If the rabbit's diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture?

A. 100
B. 140
C. 150
D. 160
E. 200
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AdarshSambare
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A rabbit on a controlled diet is fed daily 300 grams of a 17 Sep 2025, 02:15
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Let x be Feed X and y be Feed Y
0.1x + 0.15y = 38

x + y = 300
x = 300 − y

Substitute:
0.1(300 − y) + 0.15y = 38
30 − 0.1y + 0.15y = 38
0.05y = 8
y = 160 grams

Then x = 300 − 160 = 140 grams

Answer: B
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A rabbit on a controlled diet is fed daily 300 grams of a 17 Jan 2026, 19:40
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Both equations
300 = x + y
38 = x(10/100) + y(15/100)

Manipulate to eliminate fractions
100(38) = x(10/100) + y(15/100) (100)
3800 = 10x + 15Y

Scale other equation up.
15(300) = 15x + 15Y
4500 = 15x + 15Y

Use elimination to find X
4500 = 15x + 15Y
-(3800 = 10x + 15Y)
700 = 5 x
70*2 = x
140 = x
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