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dimmak
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15 Oct 2018, 10:09
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A convenience store stocks soda in 12-ounce and 24-ounce bottles. If the average capacity of all the bottles in the store is 22 ounces, then what fraction of the bottles in the store are 12 ounces?
A) 1/3
B) 1/6
C) 2/3
D) 5/6
E) 2/5
A) 1/3
B) 1/6
C) 2/3
D) 5/6
E) 2/5
15 Oct 2018, 10:25
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dimmak
A convenience store stocks soda in 12-ounce and 24-ounce bottles. If the average capacity of all the bottles in the store is 22 ounces, then what fraction of the bottles in the store are 12 ounces?
A) 1/3
B) 1/6
C) 2/3
D) 5/6
E) 2/5
A) 1/3
B) 1/6
C) 2/3
D) 5/6
E) 2/5
We can apply the weighted average formula, which says:
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...
So, we get: group average = (proportion of 12-ounce sodas in stock)(average weight of 12-ounce sodas) + (proportion of 24-ounce sodas in stock)(average weight of 24-ounce sodas)
Let F = the fraction (proportion) of 12-ounce sodas in stock
This means 1 - F = the fraction (proportion) of 24-ounce sodas in stock
We also know the weighted average of all sodas is 22 ounces.
So, we can write: 22 = (F)(12) + (1 - F)(24)
Expand: 22 = 12F + 24 - 24F
So: 22 = 24 - 12F
So: -2 = -12F
So: F = 2/12 = 1/6
Answer: B
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dimmak
A convenience store stocks soda in 12-ounce and 24-ounce bottles. If the average capacity of all the bottles in the store is 22 ounces, then what fraction of the bottles in the store are 12 ounces?
A) 1/3
B) 1/6
C) 2/3
D) 5/6
E) 2/5
A) 1/3
B) 1/6
C) 2/3
D) 5/6
E) 2/5
Let
The number of 12 ounce bottles = X and
The number of 24 ounce bottles = Y
Then, it is given in question stem that average of all the bottles are 22 ounces
so, (12*X+24*Y)/(X+Y)= 22
Solving this we get-> 12X+24Y=22X+22Y
=> 2Y=10X
=>Y/X=5
Now, we have to find what fraction of the bottles are 12 ounces=> X/(X+Y)=>1/(1+Y/X)
=> 1/(1+5)=>1/6. Hence correct option is B.
