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21 Aug 2012, 04:28
Kudos
Bookmarks
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?
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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22 Aug 2012, 10:45
Kudos
Bookmarks
rakesh.id
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.
26 Aug 2012, 07:42
Kudos
Bookmarks
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
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
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
