The price of a color printer is reduced by 30 % of its...

The price of a color printer is reduced by $30 \%$ of its original price. When it still does not sell, its price is reduced by $20 \%$ of the reduced price. The salesperson informs you that there has been a total reduction of $50 \% .$ Is the salesperson using percentages properly? If not, what is the actual percent reduction from the original price?

Key Concepts

Compound Multiplicative Effects

Compound multiplicative effects refer to the idea that applying percentage changes sequentially results in a multiplication of the remaining fractions of the initial value. For instance, a 30% reduction leaves 70% remaining, and a subsequent 20% reduction leaves 80% of the reduced price, leading to a combined effect obtained by multiplying 0.70 by 0.80.

Difference Between Additive and Multiplicative Percentage Changes

This concept highlights the common misconception of simply adding percentage decreases (such as 30% and 20% to claim a 50% reduction), while in reality, the percentages combine multiplicatively. Correctly applying this concept shows that the actual reduction is determined by the product of the individual retention percentages, often resulting in a different net percentage change from the sum of individual percentages.

Successive Percentage Reductions

Successive percentage reductions involve applying multiple discounts in sequence, where each discount is calculated on the price obtained after the previous discount, not on the original price. This concept is crucial because it demonstrates that the effect of multiple discounts is multiplicative rather than additive.

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