2009 AMC 12B Problem 2

Below is the professionally curated solution for Problem 2 of the 2009 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2009 AMC 12B solutions, or check the answer key.

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Concepts:ratio and proportion

Difficulty rating: 900

2.

Paula the painter had just enough paint for 3030 identically sized rooms. Unfortunately, on the way to work, three cans of paint fell off her truck, so she had only enough paint for 2525 rooms. How many cans of paint did she use for the 2525 rooms?

1010

1212

1515

1818

2525

Solution:

Losing 33 cans cost her 55 rooms, so 33 cans paint 55 rooms and each room needs 35\dfrac{3}{5} of a can.

For 2525 rooms she used 2535=1525 \cdot \dfrac{3}{5} = 15 cans.

Thus, the correct answer is C.

Problem 2 in Other Years