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Finding Ratio from Weighted Average

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Finding Ratio from Weighted Average [#permalink] New post 21 Aug 2012, 03:28
I know we can find the ratio of two things from their weighted average. My query: Is it possible to calculate the ratio of three things from their weighted average?

Let's take an example:

A fruit shake contains fruit pulp, milk and ice. Fruit pulp costs $5 per liter, milk costs $4 per liter, and ice costs $2 per liter. If the cost of the fruit shake is $3 per liter (weighted average of the three ingredients), is the data sufficient to find the ratio of fruit pulp : milk : ice in the fruit shake?
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Re: Finding Ratio from Weighted Average [#permalink] New post 22 Aug 2012, 09:45
rakesh.id wrote:
I know we can find the ratio of two things from their weighted average. My query: Is it possible to calculate the ratio of three things from their weighted average?

Let's take an example:

A fruit shake contains fruit pulp, milk and ice. Fruit pulp costs $5 per liter, milk costs $4 per liter, and ice costs $2 per liter. If the cost of the fruit shake is $3 per liter (weighted average of the three ingredients), is the data sufficient to find the ratio of fruit pulp : milk : ice in the fruit shake?


No, it's not possible unless you have more information. In your example, if you had 6 liters in total of fruit shake, you might have, say, 2 liters of fruit pulp, 0 liters of milk, and 4 liters of ice, or you might have 0 liters of milk, 3 liters of milk, and 3 liters of ice, among many other possibilities. So we can get different ratios from the given information.
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Re: Finding Ratio from Weighted Average [#permalink] New post 26 Aug 2012, 06:42
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Let's understand this possibility with the help of an equation

Considering two items: fruit pulp and milk
Cost of fruit pulp = $ 5 per liter
Cost of milk = $ 4 per liter
if the cost of the mixture is 4.5 liter, just assume, we can find out their ratio.
assume ratio is a:b
So, forming the equation we get-

5a + 4b = 4.5 (a+b)
.5a=.5b
a=b
therefore, a:b = 1:1

Considering three items: fruit pulp, milk and ice
Here, cost of ice = $ 2 per liter
Cost of fruit shake = $ 3 per liter
If the ratio of fruit pulp, milk and ice is a:b:c
we form the equation as follows-
5a + 4b + 2c = 3 (a+b+c)
2a+b-c=0

In this equation there are three variables. So, in no way we can find ratio of a,b,c

Note:
To find values of n variables we need n equations
to find ratio of n variables we need (n-1) equations
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Re: Finding Ratio from Weighted Average   [#permalink] 26 Aug 2012, 06:42
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Finding Ratio from Weighted Average

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