Manhattan 5lbs. Averages Q.30)

[xerocoool]

Hi Tommy,

Q) Fixer 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 12 ounces of Cereal, how much of the cereal, in ounces, is Fiber X ?

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

I am unable to understand the question (or the right way to proceed), could you please explain me the general idea in short.

Thanks
xero

[tommywallach]

Hey Xero,

This is a weighted average question. The mixed cereal is 65% fiber. That's twice as close to the Fiber Max Cereal (70%) as it is to the Fiber X cereal (55%). You can see that because 65 is 5 away from 70, but 10 away from 55. That means we have twice as much Fiber Max as Fiber X (because the amount of fiber in the mix is twice as close to the Fiber Max amount as to the Fiber X amount). So if we have 12 ounces altogether, we have 8 ounces of Fiber Max and 4 ounces of Fiber X.

Hope that helps!

-t

[xerocoool]

Hi Tommy,

Thanks ! that helps :)

xero

[tommywallach]

Glad to do it!

-t

[kg2576]

On this question, I tried to set it up algebraically based on the first approach in the back of the book. I made the following mistake in my denominator:

0.55x + 0.70m / 12 = 0.65

What have I missed in the approach? Isn't x + m = 12 based on the question? Thanks.

[muhammad_shamir90]

In addition to above explanations, the average is close to fiber max percent(65 close to 70 than 55).. so ounces can never be distributed equally in the case and we can directly cross any thing above 6 ounces, including 6, as fiber x should be less than 6. option a and b left. apply weighted avg formula to get that.

[tommywallach]

Hey Kg,

I don't see any problem with that setup. But you'll still need the other equation (x + m = 12), because as it stands you only have one equation with two variables in it.

-t