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# An elephant in a zoo is fed a diet that consists solely of a mixture

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Re: An elephant in a zoo is fed a diet that consists solely of a mixture [#permalink]
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Bunuel wrote:
An elephant in a zoo is fed a diet that consists solely of a mixture of 2 different foods, Food A and Food B, which contains 30 percent fat and 10 percent fat, respectively. The elephant consumes a total of 50 pounds of food daily. How many pounds of Food A are in the elephant's daily food mixture if the mixture contains exactly 11 pounds of fat?

(A) 50
(B) 30
(C) 20
(D) 9
(E) 2

I found a neat trick that helped me solve this question quickly.

The final mixture contains 11 pounds of fat.

$$\frac{11}{50}*100 = 22%$$

From this we can infer that more of food A is present in the mixture. That is A is more than 25 pounds.
If the foods were mixed in the ratio of 1:1 then the resultant would be 20% of fat (Avg of 30 and 10).
If the entire mixture was A, then the fat would be 30 percent. Which is not the case.

So the answer should be B.
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Re: An elephant in a zoo is fed a diet that consists solely of a mixture [#permalink]
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Kudos
This is a problem of aggregate and the answer can be given as

Take A be the weight of food A given to the elephant and B be the weight of food B given to the elephant

A+B=50
0.3A+0.1B=11

Solving A= 30

Hence A
Re: An elephant in a zoo is fed a diet that consists solely of a mixture [#permalink]
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