Bunuel wrote:
A soft drink company currently sells its most popular product in one-liter containers for $3, yielding a 20% profit margin on the cost. If cost is proportional to volume, by what percent should the company reduce the volume of the container to yield a 50% profit margin on the cost, assuming the selling price remains the same?
A. 10%
B. 20%
C. 25%
D. 33%
E. 50%
OFFICIAL SOLUTION
Begin by finding the cost of the 1-liter container: 1.2c = 3, and c = 2.5. Next, let’s figure out how much the product cost should be to create the 50% profit margin: 1.5x = 3, and x = 2. Since cost is proportional to volume, the percent change in cost is the same as the percent change in volume: \(\frac{(2.5 - 2.0)}{2.5} = \frac{0.5}{2.5}\)= 20%.
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