Problem 1 · 2006 AMC 8
Easy
Arithmetic & Operations
estimation
Mindy made three purchases for $1.98, $5.04, and $9.89. What was her total, to the nearest dollar?
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Answer: D — $17.
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Hint 1 of 2
"To the nearest dollar" is permission to throw away the pennies — you don't need an exact total. Each price is already hugging a whole dollar.
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Hint 2 of 2
Rounding first, then adding, is far lighter than adding first, then rounding — and here it gives the same answer because each price is so close to a whole number.
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Approach: round each first, then add
- The question only wants the nearest dollar, so round before doing any arithmetic: $1.98 → 2, $5.04 → 5, $9.89 → 10.
- 2 + 5 + 10 = 17.
- Why this is safe: each price is within about 10 cents of a whole dollar, so the rounding errors are tiny and can't push the sum across a dollar boundary. When numbers sit close to round values, round first — you'll see this trick on every "estimate the total" question.
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