AMC 10 · 2006 · #9
Grade 6 rate-ratioPick an answer.
AMC 10 2006 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
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
Only lemon juice (25) and sugar (386) carry calories, so the whole batch holds 411 calories.
The whole batch holds the calories of its ingredients combined.
4.NBT.B.4Identify SubproblemsAdd up the grams
The masses add up too: 100 plus 100 plus 400 makes 600 grams of lemonade in all.
Every gram poured in stays in, so the total mass is just the sum.
4.NBT.B.4Identify SubproblemsScale down to 200 grams
200 out of 600 grams is one-third of the batch, so the serving holds one-third of 411, namely 137.
One-third of the lemonade carries one-third of the calories.
One third of the lemonade carries one third of the calories.
▸ Why?
The drink is uniform, so any share of it holds that same share of everything inside.
▸ Why?
A fraction of a quantity is that quantity cut into equal shares and one taken.
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