Problem 15 · 2022 AMC 8
Medium
Fractions, Decimals & Percents
unit-rateestimate-and-pick
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Answer: C — 3 ounces.
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Hint 1 of 2
You want the cheapest per ounce, not the cheapest sticker price. So at each weight only the lowest dot can possibly win — ignore every dot above it.
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Hint 2 of 2
Price ÷ weight is the slope of the line from the origin to a dot — flatter line = better deal. So find the dot you could draw the most gently-sloped line to. Then check just the five lowest dots by dividing.
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Approach: only the lowest dot per weight matters; smallest price÷weight wins
- Insight: a higher dot at the same weight is strictly worse, so for each weight keep only the lowest dot — that trims 30 points down to 5 candidates.
- Now compare price ÷ weight for those 5. Reading the plot: 1 oz ≈ $1.25 → 1.25; 2 oz ≈ $2 → 1.00; 3 oz ≈ $2.5 → ≈0.83; 4 oz ≈ $3.9 → ≈0.97; 5 oz ≈ $4.5 → ≈0.90.
- The 3-ounce option is cheapest per ounce (≈$0.83/oz). Answer: 3 ounces.
- You'll see this again: price-per-ounce is the slope of the line from the origin to a dot — the best deal is the dot you can reach with the flattest such line, which you can often spot by eye before dividing.
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