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−D1D2−D2D3−D2D1+D1D2D3, then the choices are:
.20+.20+.10−.04−.02−.02+.004=.424 and .40+.05+.05−.02−.02−.0025+.001=.4585.
The saving is .0345⋅10,000=345 dollars.