7Dr. Emily Carter identified fossil spores in three sediment layers: upper (18 samples), middle (42), lower (60). She wants to organize them into display cases such that each case has the same number of samples from each layer, with no samples left. What is the maximum number of display cases she can use? - AdVision eCommerce
7Dr. Emily Carter’s Discovery: Maximizing Display Cases with Equal Fossil Spore Samples from All Sediment Layers
7Dr. Emily Carter’s Discovery: Maximizing Display Cases with Equal Fossil Spore Samples from All Sediment Layers
In a groundbreaking study, paleontologist Dr. Emily Carter identified fossil spores in three distinct sediment layers from a key geological site: 18 samples from the upper layer, 42 from the middle layer, and 60 from the lower layer. These samples offer invaluable clues about ancient ecosystems and environmental changes across time. Now, Dr. Carter seeks to create equal, informative display cases for public engagement and research — each containing the same number of fossil spores from every sediment layer, with no samples left over. The challenge: what is the maximum number of display cases she can construct under these conditions?
Understanding the Context
Understanding the Problem
To ensure each display case has identical representation from all three layers, the number of samples from each layer per case must evenly divide the total counts: 18 upper, 42 middle, and 60 lower fossils. Thus, the critical question becomes: What is the largest number of cases such that each layer’s samples are fully and equally distributed?
This requires finding the greatest common divisor (GCD) of the three sample counts: 18, 42, and 60.
Image Gallery
Key Insights
Finding the Greatest Common Divisor (GCD)
We compute the GCD to determine the maximum number of display cases possible with no leftover samples:
- Prime factorization:
- 18 = 2 × 3²
- 42 = 2 × 3 × 7
- 60 = 2² × 3 × 5
- 18 = 2 × 3²
The common prime factors are 2 and 3, each to the lowest power present:
- Minimum power of 2 = ²¹ → 2¹
- Minimum power of 3 = ³¹ → 3¹
Thus:
GCD(18, 42, 60) = 2 × 3 = 6
🔗 Related Articles You Might Like:
📰 Nyt Connections Hints October 23 📰 Wordle Hint May 12 📰 Vpn Security News 📰 Fractions In The Number Line 4271113 📰 Whats Worse Than A Cumpster The Humiliating Truth Behind Their Rise And Fall 4303866 📰 Revealed Why Millions Choose Microsoft Office Portable Over The Full Version 5574062 📰 Hot Free Discover The Best Driving Games You Can Play For Free Now 8263392 📰 2 Player Spellen 6696742 📰 Kim Min Hee 2833123 📰 Hakkur Exposes Secrets No One Talks About 8884451 📰 Youll Never Believe What Happened When We Saved That Dying Dogyou Must Watch 2204088 📰 Crzay Game Finally Releasedplayers Are Going Wild Over This Bootloader 9055795 📰 The Batman 2 Trailer 2517422 📰 Limited English Proficiency This Science Backed Hack Will Transform Your Skills Overnight 9475581 📰 Samsung Electronics Stock 2462865 📰 Brian Mcknight Son 4946688 📰 Pecos Logins Secrets How Hackers Are Exploiting Login Access Every Minute 497426 📰 Unlock The Power Of The Pisces And Libra Connectionlove Intuition And Harmony Combined 2658344Final Thoughts
Organizing the Display Cases
Dr. Carter can therefore prepare 6 display cases — the maximum number possible — each containing:
- 18 ÷ 6 = 3 fossil spore samples from the upper layer
- 42 ÷ 6 = 7 fossil spore samples from the middle layer
- 60 ÷ 6 = 10 fossil spore samples from the lower layer
This balanced arrangement ensures each case is rich, consistent, and scientifically meaningful.
Why This Matters
By aligning her display strategy with mathematical precision, Dr. Carter not only honors scientific rigor but also enhances educational storytelling. Using the GCD to balance sample distribution ensures that each case delivers equal scientific value — a hallmark of thoughtful curation in paleontology.
Conclusion
The maximum number of display cases Dr. Emily Carter can create — with uniform, non-empty representation of fossil spores from all three sediment layers — is 6. This achievement reflects both scientific ingenuity and practical display planning, setting a powerful example for interdisciplinary research communication.
