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

Current total volume = (current number of bottles)(average volume) = 48*35 = 1680 ounces.

We can PLUG IN THE THE ANSWERS, which represent the number of 40-ounce bottles that must be sold to reduce the average to 25 ounces per bottle.

Answer choice D: 32
After 32 40-ounce bottles are sold, the remaining total volume = 1680 - (32*40) = 1680 - 1280 = 400 ounces.
Remaining number of bottles = 48-32 = 16.
Average volume for the remaining 16 bottles = 400/16 = 25.
Success!

The correct answer is D.

And there's always our good friend, the number line. Initially, we have 20-ounce and 40-ounce bottles and an overall average of 35 ounces per bottle. If we plot these numbers on a number line, we'll have the following:





This tell us that we'll have a ratio of 15:5 or 3:1 in favor of 40-ounce bottles. (Because the initial average is closer to 40, those bottles are exerting a great pull on the overall average.) Call the number of 40-ounce bottles '3x' and the number of 20-ounce bottles 'x.'

40-ounce bottles: 3x
20-ounce bottles: x
Total: 48

3x + x = 48. 4x = 48. x = 12; 3x = 36. So we're starting with 36 of the 40-ounce bottles and 12 of the 20-ounce bottles.

We want to have an average of 25 ounces. Now the number line will look like this:




So now we'll have a 5:15 or 1:3 ratio, and this time we'll have more 20-ounce bottles. We know from our initial calculation that we had 12 of the 20-ounce bottles. If we have 1/3 as many 40-ounce bottles as we have 20-ounce bottles, we'll have 4 of the 40-ounce bottles.

Initially we had
40-ounce bottles:36
20-ounce bottles: 12

After the change, we need
40-ounce bottles: 4
20-ounce bottles: 12

To get from 36 to 4, we'll have to sell 32 bottles.

Answer is D