Comments on How can school children intuit why over 100, D is larger? But under 100, D% is larger?
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How can school children intuit why over 100, D is larger? But under 100, D% is larger?
I can prove the Rule of 100 algebraically, below. But my school kids are hankering after intuition, and a plainer explanation.
Follow the Rule of 100
Should discounts be percentages or absolutes?
Consider a \$150 blender. Should you offer 20% off? Or an equivalent \$30 off?
Answer:
- **Over \$100?** Give absolutes (e.g., \$30)
- Under \$100? Give percents (e.g., 20%)
In both cases, you show the higher numeral. For a \$50 blender, 20% off is the same as \\$10 off — yet 20% is more persuasive because it’s a higher numeral. For a \$150 blender, the absolute discount (\\$30 off) is a higher numeral (González, Esteva, Roggeveen, & Grewal, 2016).
References
González, E. M., Esteva, E., Roggeveen, A. L., & Grewal, D. (2016). Amount off versus percentage off—when does it matter?. Journal of Business Research, 69(3), 1022-1027.
Let d = discount, p = price. Then $d, p > 0$ because there is no free lunch and the quotation is expatiating on discounts. Then
\$ off vs. % off $\iff p - d \quad \text{ vs } \quad p - (d/100)p \iff -d \quad \text{ vs } \quad -dp/100 \iff 1 \quad \text{ vs } \quad p/100 \iff p \quad \text{ vs } \quad 100. $
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