A fruit juice company altered its packaging from boxes measuring centimeters to boxes measuring centimeters. If the price for a box of juice remained unchanged and all boxes are filled to capacity with juice, by approximately what percent did the price of the juice per unit of volume decrease?
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Wait, is the answer just the % change in volume? I got 16.67% by doing (1200-1000)/1200. Is that right?
Yes, since price stays the same, the price per volume drops by the same % that volume increases.
Careful: the base should be the new volume? I did 200/1000 and got 20%, which is a trap answer.
Tricky wording. I almost picked 20% because I compared to the old volume. Need to remember price per unit volume is inversely proportional to volume.
Same here! The answer choices having both 16.67 and 20 is evil.
This one took me 3 minutes. The volume goes from 1000 to 1200, so the new price per cm^3 is 1000/1200 of the old. That's a 1/6 decrease, so 16.67%. The math is simple but the wording is a bit dense.
What it tests
Your ability to compute percentage change, percentage of a whole, and to work backwards from a final value.
Common trap
Treating successive percentage changes as additive — a 10% rise then a 10% fall is not back to the start.