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2005 AMC 12A Problem 4

Problem 4 of 25EasierCounting & Probability

A store normally sells windows at $100\$100 each. This week the store is offering one free window for each purchase of four. Dave needs seven windows and Doug needs eight windows. How many dollars will they save if they purchase the windows together rather than separately?

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Solution

Buying separately, Dave gets 77 windows by paying for 66 ($600\$600), and Doug gets 88 by paying for 77 ($700\$700), for a total of $1300.\$1300. Buying together, they need 1515 windows: paying for 1212 yields 33 free, for a cost of $1200.\$1200. The savings are $1300$1200=$100.\$1300 - \$1200 = \$100. Thus, the correct answer is A.

More practice

Concepts: basic counting

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.