A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles must be sold for the average volume per bottle to be reduced to 25 ounces if no 20 ounce bottles are sold?a)10b)20c)30d)32e)34Correct answer is option 'D'. Can you explain this answer?

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A convenience store currently stocks 48 bottles of mineral water. The bottles have two sizes of either 20 or 40 ounces each. The average volume per bottle the store currently has in stock is 35 ounces. How many 40 ounce bottles must be sold for the average volume per bottle to be reduced to 25 ounces if no 20 ounce bottles are sold?

a)
10
b)
20
c)
30
d)
32
e)
34

Correct answer is option 'D'. Can you explain this answer?

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A convenience store currently stocks 48 bottles of mineral water. The ...

Let x = the number of 20 oz. bottles 48 – x = the number of 40 oz. bottles The average volume of the 48 bottles in stock can be calculated as a weighted average:

Therefore there are 12 twenty oz. bottles and 48 – 12 = 36 forty oz. bottles in stock. If no twenty oz. bottles are to be sold, we can calculate the number of forty oz. bottles it would take to yield an average volume of 25 oz:
Let n = number of 40 oz. bottles

(12)(20) + 40n = 25n + (12)(25)
15n = (12)(25) – (12)(20)
15n = (12)(25 – 20)
15n = (12)(5)
15n = 60
n = 4
Since it would take 4 forty oz. bottles along with 12 twenty oz. bottles to yield an average volume of 25 oz, 36 – 4 = 32 forty oz. bottles must be sold. The correct answer is D.

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A convenience store currently stocks 48 bottles of mineral water. The ...

To solve this problem, we can use the concept of weighted averages.

Let's assume that x represents the number of 40 ounce bottles that need to be sold.

Step 1: Calculate the total volume of the current stock
The store currently has 48 bottles of mineral water, and the average volume per bottle is 35 ounces. Therefore, the total volume of the current stock can be calculated as:
48 bottles * 35 ounces/bottle = 1680 ounces

Step 2: Calculate the total volume after selling x 40 ounce bottles
If x 40 ounce bottles are sold, the total volume of the remaining stock can be calculated as:
(48 - x) bottles * 35 ounces/bottle = (1680 - 40x) ounces

Step 3: Set up the equation for the new average volume
To find the new average volume per bottle, we need to divide the total volume after selling x 40 ounce bottles by the total number of bottles remaining. The equation can be set up as:
(1680 - 40x) ounces / (48 - x) bottles = 25 ounces/bottle

Step 4: Solve the equation
We can now solve the equation to find the value of x:
(1680 - 40x) / (48 - x) = 25

To simplify the equation, we multiply both sides by (48 - x):
(1680 - 40x) = 25(48 - x)
1680 - 40x = 1200 - 25x
15x = 480
x = 32

So, 32 40 ounce bottles must be sold for the average volume per bottle to be reduced to 25 ounces. Therefore, the correct answer is option D.

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