AMC 10 · 2006 · #6
Grade 6 rate-ratioPick an answer.
Calories are spread evenly through the lemonade, so what matters is the calories-per-gram rate. Find the total calories and the total grams of the whole batch, then scale that rate down to the 200-gram serving. Splitting the work into 'total calories' and 'total grams' keeps each number easy.
Add up the calories
Adding the calories gives 411.
The whole batch holds the calories of its ingredients combined.
4.NBT.B.4Identify SubproblemsAdd up the grams
Adding the weights, including the calorie-free one, gives 600.
Every gram poured in stays in, so the total mass is just the sum.
4.NBT.B.4Identify SubproblemsScale down to 200 grams
The serving is one third of the batch, giving 137.
One-third of the lemonade carries one-third of the calories.
One third of the lemonade carries one third of its calories.
▸ Why?
The mixture is uniform, so any share of the weight carries the same share of everything in it.
▸ Why?
The batch is exactly its ingredients put together, so its calories are their calories added.
When something is mixed evenly, a serving carries the same fraction of the calories as it is of the whole batch.
- Add up the calories
- Add up the grams
- Scale down to 200 grams