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Problem 66

AMC 10/12, early questions

Algebra Difficulty 3.2 Find the answer

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)}\ $360$

Your answer

Official 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 $5760 - 5415 = \fbox{\textbf{(D)} \textdollar{345}}$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.