Art of Problem Solving

1955 AHSME Problems/Problem 22: Difference between revisions

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The positive difference between the offers is therefore <math>5760 - 5415 = \fbox{\textbf{(D)} \textdollar{345}}</math>
The positive difference between the offers is therefore <math>5760 - 5415 = \fbox{\textbf{(D)} \textdollar{345}}</math>
== See Also ==
{{AHSME box|year=1955|num-b=21|num-a=23}}
{{MAA Notice}}

Latest revision as of 22:14, 9 August 2020

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

See Also

1955 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 21
Followed by
Problem 23
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
All AHSME Problems and Solutions


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