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? - Redraw
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:
📰 The Phantom Revealed: Is This the Movie Behind Every Viral Mystery? 📰 From Ghostly Whispers to Centering Fear: What ‘The Phantom’ Really Means 📰 How The Phantom Changed the Game—Shocking Facts You Must See! 📰 This 914 Area Code Beaten The Gridwhat No One Sees 1195121 📰 Dolar Hoje Real Brasileiro 4325261 📰 Grab Xbox Game Pass Ultimate Unlock These 5 Ultra Beloved Games Today 310685 📰 Epl Football Teams 3950156 📰 Meaning Of Straightforwardness 345552 📰 These Sun Dresses Are Lightweight Scandalous And Perfect For Sunset Glam 2390918 📰 Brown Jordans The Secret Hype Shoe Everyones Trying To Own In 2024 9835906 📰 Are The Rothschilds Jewish 7388229 📰 This Java Semaphore Hack Ruby Style Blasts Java Performance In Seconds 4747803 📰 Breaking Shocking Health Data Privacy Leak Exposes 100 Million Patients 350508 📰 Charleston Webcams 8657755 📰 High 5 Casino Revealed The 5 Best Secrets Every Gamer Needs To Know 6000537 📰 You Wont Believe What Happened On The Historic Bridge Raceshocking Twist At The Finish Line 7242370 📰 Golf Near Me 5774183 📰 Watch The Crow 2024 6472213Final 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.
