Problem 13 · 1990 AJHSME
Hard
Arithmetic & Operations
round-uprate
One proposal for new postage rates for a letter was 30 cents for the first ounce and 22 cents for each additional ounce (or fraction of an ounce). The postage for a letter weighing 4.5 ounces was
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Answer: C — 1.18 dollars.
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Hint 1 of 2
The sneaky words are 'or fraction of an ounce' — a half-ounce still costs a full extra charge. So you can't just multiply by 4.5; you have to round each leftover bit UP to a whole charge.
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Hint 2 of 2
Separate the bill into 'first ounce' (special price) plus 'each additional ounce' (rounded up). This round-up-to-the-next-whole rule is how taxis, parking, and shipping all charge.
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Approach: first ounce at one rate, the rest rounded up to whole ounces
- The pricing has two parts: the first ounce is 30¢, flat. After that, 4.5 − 1 = 3.5 ounces remain.
- Here's the trap: 'or fraction of an ounce' means that leftover 0.5 ounce is billed as a *whole* extra ounce. So 3.5 additional ounces round UP to 4 charges of 22¢.
- Total = 30 + 4×22 = 30 + 88 = 118¢ = $1.18.
- *Worth keeping:* whenever a rate says 'or any part thereof,' round each chunk up to the next whole unit — same idea as parking 'per hour or part of an hour.'
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