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
