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2005 AMC 10A Problem 5

Problem 5 of 25EasierAlgebraCounting & 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

Alone, Dave pays for 66 windows and receives one free to reach 7,7, costing $600;\$600; Doug pays for 77 and receives one free to reach 8,8, costing $700.\$700. Separately they pay $1300.\$1300. Together they need 1515 windows: buying 1212 yields 33 free, for $1200.\$1200. The savings are 1300−1200=1001300 - 1200 = 100 dollars. Thus, the correct answer is A.

More practice

Concepts: money · basic counting

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