Problem 8 · 1993 AJHSME
Medium
Ratios, Rates & Proportions
rate
To control her blood pressure, Jill's grandmother takes one half of a pill every other day. If one supply of medicine contains 60 pills, then the supply would last approximately
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Answer: D — 8 months.
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Hint 1 of 2
The pills last so long because of a double stretch: each dose is only half a pill, AND each dose covers two days. Both effects multiply the days, so handle them one at a time.
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Hint 2 of 2
Chain the units: pills → doses → days. Half-pill doses mean twice as many doses as pills; every-other-day means twice as many days as doses.
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Approach: convert pills → doses → days, step by step
- Each dose is ½ a pill, so 60 pills make 60 ÷ ½ = 120 doses. (Dividing by a half doubles the count — half-size pieces means twice as many.)
- Each dose covers 2 days ('every other day'), so 120 doses last 120 × 2 = 240 days. A year is 365 days and 240 ÷ 30 ≈ 8, so the supply lasts about 8 months.
- Why this transfers: 'half a pill every other day' hides two doublings. Walking through one conversion at a time — and naming each unit — keeps you from accidentally cancelling them or doing only half the job.
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