2006 AMC 12B Problem 6

Attempt Problem 6 of the 2006 AMC 12B 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 2006 AMC 12B solutions, or check the answer key.

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

6.

Francesca uses 100100 grams of lemon juice, 100100 grams of sugar, and 400400 grams of water to make lemonade. There are 2525 calories in 100100 grams of lemon juice and 386386 calories in 100100 grams of sugar. Water contains no calories. How many calories are in 200200 grams of her lemonade?
129129
137137
174174
223223
411411
Answer: B
Concepts:ratio and proportion
Small hint:
Find the total calories and total grams of the whole batch first
Big hint:
200200 grams is one third of the full 600600-gram batch
Solution:
The full batch weighs 100+100+400=600100 + 100 + 400 = 600 grams and contains 25+386=41125 + 386 = 411 calories.
Since 200200 grams is one third of the batch, it has 4113=137\frac{411}{3} = 137 calories.
Thus, the correct answer is B.
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