2006 AMC 12B Problem 6

Below is the professionally curated solution for Problem 6 of the 2006 AMC 12B, 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.

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Concepts:ratio and proportion

Difficulty rating: 1070

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 full batch weighs $100 + 100 + 400 = 600$ grams and contains $25 + 386 = 411$ calories.

Since $200$ grams is one third of the batch, it has $\frac{411}{3} = 137$ calories.

Thus, the correct answer is B.

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