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2006 AMC 10B Problem 9

2006 AMC 10B Problem 9AMC 10 Step by Step

Name: Date: September 13, 2026

Ratios, Percents & Averages · difficulty 1 of 5 · about 1 min · position P1-10

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?

A)
$129$
B)
$137$
C)
$174$
D)
$233$
E)
$411$

Answer

Key insight

The whole batch is 600 grams with 25 + 386 = 411 calories, and 200 grams is one third of it, so 411/3 = 137.

Solution

Total mass of the lemonade: $100 + 100 + 400 = 600$ grams.

Total calories: $25$ from the lemon juice, $386$ from the sugar, $0$ from the water, so $411$ calories.

A $200$ -gram serving is $\frac{200}{600} = \frac{1}{3}$ of the batch, so it contains $\frac{411}{3} = 137$ calories.

The answer is $\boxed{\textbf{(B)}\ 137}$ .

Why this works

Calories are distributed uniformly through a well-mixed drink, so any portion has the same calories-per-gram rate as the whole. Compute total calories and total mass (including the calorie-free water, which still adds mass), then scale.

The trap

Forgetting the 400 grams of water in the total mass, which gives 411 calories for 200 grams.

Common mistakes

Forgetting the 400 grams of water in the total mass, which gives 411 calories for 200 grams.
Adding only the lemon juice and sugar masses ( $200$ g) and answering $411$ , or averaging $25$ and $386$ carelessly.

Techniques

Set up the equation/formula and compute; no special trick needed