A convenience store stocks soda in 12-ounce and 24-ounce bottles.

BTGModeratorVI wrote: ↑

Fri Jun 05, 2020 11:42 am

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

Answer: B
Source: Manhattan prep

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

BTGModeratorVI wrote: ↑

Fri Jun 05, 2020 11:42 am

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

Answer: B

Solution:

We can let a = the number of 12-ounce bottles and b = the number of 24-ounce bottles. We can create the equation:

12a + 24b = 22(a + b)

12a + 24b = 22a + 22b

2b = 10a

b = 5a

Thus, a/(a + b) = a/(a + 5a) = a/6a = 1/6 of the bottles are 12 ounces.

Answer: B