2005 AMC 10B Problem 1

Attempt Problem 1 of the 2005 AMC 10B below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2005 AMC 10B solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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
Answer: A
Concepts:moneyratio and proportion
Small hint:
Find the total cost and the total revenue separately
Big hint:
The bars come in 200200 groups of five and 500500 pairs
Solution:
The troop buys 1000÷5=2001000 \div 5 = 200 groups of five bars, costing 200⋅2=400200 \cdot 2 = 400 dollars.
They sell 1000÷2=5001000 \div 2 = 500 pairs of bars, earning 500⋅1=500500 \cdot 1 = 500 dollars.
The profit is $500−$400=$100.\$500 - \$400 = \$100.
Thus, A is the correct answer.
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