# 1955 AHSME Problems/Problem 22

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## Problem 22

On a $\textdollar{10000}$ 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: $\textbf{(A)}\ \text{nothing at all}\qquad\textbf{(B)}\ 440\qquad\textbf{(C)}\ 330\qquad\textbf{(D)}\ 345\qquad\textbf{(E)}\ 360$

## Solution

In order to solve this problem, we can simply try both paths and finding the positive difference between the two.

The first path goes $10,000 * 0.8 = 8,000 * 0.8 = 6400 * 0.9 = \textbf{5760}$

The second path goes $10,000 * 0.6 = 6,000 * 0.95 \text{ or } (1 - 0.05) = 5700 * 0.95 = \textbf{5415}$

The positive difference between the offers is therefore $5760 - 5415 = \fbox{\textbf{(D)} \textdollar{345}}$

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