2006 AMC 10B Problem 9

Below is the professionally curated solution for Problem 9 of the 2006 AMC 10B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2006 AMC 10B solutions, or check the answer key.

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Concepts:ratio and proportion rate

Difficulty rating: 1000

Francesca uses $100$ grams of lemon juice, $100$ grams of sugar, and $400$ grams of water to make lemonade. There are $25$ calories in $100$ grams of lemon juice and $386$ calories in $100$ grams of sugar. Water contains no calories. How many calories are in $200$ grams of her lemonade?

$129$

$137$

$174$

$223$

$411$

Solution:

The lemonade totals $100+100+400=600$ grams containing $25+386=411$ calories.

In $200$ grams there are $411\cdot\tfrac{200}{600}=\tfrac{411}{3}=137$ calories.

Thus, the correct answer is B.

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