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2006 AMC 10B Problem 9

Problem 9 of 25EasierAlgebra

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?

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Solution

The lemonade totals 100+100+400=600100+100+400=600 grams containing 25+386=41125+386=411 calories. In 200200 grams there are 411⋅200600=4113=137411\cdot\tfrac{200}{600}=\tfrac{411}{3}=137 calories. Thus, the correct answer is B.

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Concepts: ratio and proportion · rate

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.