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Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. Sheldon co

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Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. Sheldon co  [#permalink]

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New post 30 Aug 2018, 00:29
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Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. Sheldon combines an amount of the two cereals in a single bowl of mixed cereal that is 65% fiber. If the bowl contains a total of 12 ounces of cereal, how much of the cereal, in ounces, is Fiber X?

(A) 3
(B) 4
(C) 6
(D) 8
(E) 9

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Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. Sheldon co  [#permalink]

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New post 30 Aug 2018, 00:57
Bunuel wrote:
Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. Sheldon combines an amount of the two cereals in a single bowl of mixed cereal that is 65% fiber. If the bowl contains a total of 12 ounces of cereal, how much of the cereal, in ounces, is Fiber X?

(A) 3
(B) 4
(C) 6
(D) 8
(E) 9


Given, Total content of cereal=12 ounce
Resultant fiber content in the mixture=65%
Let a and b are the content of fiber X and fiber Max respectively in the mixture.

Using weighted average method,
\(\frac{0.55a+0.70b}{a+b}=0.65\)
Or, 55a + 70b= 65a + 65b
Or, 10a = 5b
Or, a:b=1:2

So, cereal in fiber x=\(\frac{1}{1+2}*12\)=4

Ans. (B)

We can solve using allegation method also.
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Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. Sheldon co  [#permalink]

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New post 31 Aug 2018, 22:53
Fiber X = 55%
Fiber Max Cereal = 70%

Fiber X + Fiber Y = 65% of 12 ounce

=65 x 12/100 = 7.8 ounce of fiber

Fiber X in 12 ounce
= 55/100 x 7.8
=4.29(Approximate value). Hence I chose B.

Is this method correct? :|

Also, could someone show me how to solve this with allegation method?
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Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. Sheldon co  [#permalink]

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New post 01 Sep 2018, 01:32
1
x 0,55 ------0,05
--------0,65------
y 0,7 ------0,1

X/Y = 1/2.
X+Y= 12
-----> X= 4
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Re: Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. Sheldon co  [#permalink]

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New post 01 Sep 2018, 02:02
Let x and y be the amounts of cereal mixed.
Then x+y=12...(1)
.55x+.7y=.65*12....(2)
Solving we get
x=4,so B is the correct choice.


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Re: Fiber X cereal is 55% fiber. Fiber Max cereal is 70% fiber. Sheldon co   [#permalink] 01 Sep 2018, 02:02
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