2005 AMC 12A Problem 4

Below is the professionally curated solution for Problem 4 of the 2005 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2005 AMC 12A solutions, or check the answer key.

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Concepts:basic counting

Difficulty rating: 1200

A store normally sells windows at $\$100$ 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?

$100$

$200$

$300$

$400$

$500$

Solution:

Buying separately, Dave gets $7$ windows by paying for $6$ ( $\$600$ ), and Doug gets $8$ by paying for $7$ ( $\$700$ ), for a total of $\$1300.$

Buying together, they need $15$ windows: paying for $12$ yields $3$ free, for a cost of $\$1200.$

The savings are $\$1300 - \$1200 = \$100.$

Thus, the correct answer is A.

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