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Home » Solution: First, find the least common multiple of 12 and 18. - ClickBalance

Solution: First, find the least common multiple of 12 and 18. - ClickBalance

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 A historian analyzes a 2,400-year-old calendar system that cycles every 140 years. If a significant celestial event occurred in year 58 of the first cycle, and another in year 110 of the 14th cycle, what is the absolute difference in years between the two events? (Note: 14th cycle starts at (14 – 1) × 140 = 1820, so year 1 = 0)

📌 First, find year number of event at year 58 of first cycle: since cycles are 140 years, and first cycle starts year 0, event at year 58.

📌 14th cycle starts at 13 × 140 = 1820; so year 110 of 14th cycle is 1820 + 110 = <<1820+110=1930>>1930.

📌 Event 1: year 58, Event 2: year 1930.

📌 Absolute difference: 1930 – 58 = <<1930-58=1872>>1,872 years.

📌 #### 1872A climatologist analyzing satellite data observes that a particular Arctic region has lost ice cover at an average rate of 13.1 billion tons per year over the past 32 years. If the total ice mass lost during this period is equivalent to 420 billion tons, and the loss has been accelerating uniformly by 0.4 billion tons more per year each year, how much ice was lost in the final year?

📌 This is a uniformly accelerating sequence where total loss = sum of an arithmetic series.

📌 Let the first year’s loss be \( a \), common difference \( d = 0.4 \), number of terms \( n = 32 \), and total loss = 420 billion tons.

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