2005 AMC 12B Problem 1

Below is the professionally curated solution for Problem 1 of the 2005 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2005 AMC 12B solutions, or check the answer key.

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Concepts:ratio and proportionmoney

Difficulty rating: 890

1.

A scout troop buys 10001000 candy bars at a price of five for $2.\$2. They sell all the candy bars at a price of two for $1.\$1. What was their profit, in dollars?

100100

200200

300300

400400

500500

Solution:

The troop buys 1000÷5=2001000 \div 5 = 200 groups of five bars, costing 2002=400200 \cdot 2 = 400 dollars.

They sell 1000÷2=5001000 \div 2 = 500 pairs of bars, earning 5001=500500 \cdot 1 = 500 dollars.

The profit is 500400=100500 - 400 = 100 dollars.

Thus, the correct answer is A.

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