Problem: On a $10,000 order a merchant has a choice between three successive discounts of 20%,20%, and 10% and three successive discounts of 40%,5%, and 5%. By choosing the better offer, he can save:
Answer Choices:
A. nothing at all
B. $400
C. $330
D. $345
E. $360
Solution:
Since a single discount D, equal to three successive discounts D1​,D2​, and D3​, is D=D1​+D2​+D3​−D1​D2​−D2​D3​−D2​D1​+D1​D2​D3​, then the choices are:
​.20+.20+.10−.04−.02−.02+.004=.424 and .40+.05+.05−.02−.02−.0025+.001=.4585.​
The saving is .0345â‹…10,000=345 dollars.