Problem 104 - Elementary and Intermediate Algebra

Question

History. Plato, a famous Greek philosopher, died in 347 B.C. at the age of \(81 .\) When was he born?

Step-by-Step Solution

Answer

Plato was born in 428 B.C.

Step 1: Understand the Information

We know that Plato died in 347 B.C. and lived for 81 years. To find his birth year, we will have to subtract his age at death from his year of death.

Step 2: Use B.C. Era Logic

In the B.C. era (Before Christ), the years count backwards. Thus, subtracting a smaller number from a larger one moves us back in time. Therefore, to find a birth year, we subtract the age from the year of death.

Step 3: Perform the Calculation

Subtract his age from the year he died: \[ 347 - 81 \]Calculate the difference: \[ 347 - 81 = 266 \]So, Plato was born in 428 B.C.

Key Concepts

B.C. era calculations

The calculation of dates in B.C. (Before Christ) time can be confusing because the numbering of years goes backwards. Instead of moving forward from a smaller number to a bigger one, as we do in the current AD or CE calendrical system, B.C. goes from larger to smaller numbers. For example, the year 400 B.C. is earlier than 300 B.C. in history's timeline.
This can be tricky when doing arithmetic, especially subtraction, since it is not as intuitive as modern times. Therefore, if you want to calculate someone's birth year knowing the death year and the age at that time, you need to subtract their age from the year they died. In the exercise, for instance, Plato died in 347 B.C. at 81 years old, so his birth year was calculated as 347 B.C. minus 81, resulting in 428 B.C.

ancient history

Understanding ancient history is crucial for grasping how the world developed over millennia. The B.C. era marks times before the traditionally accepted birth year of Jesus Christ, which is why it counts backwards.
History from this era identifies great civilizations such as Ancient Greece, where philosophers like Plato emerged. These times were characterized by vast intellectual and cultural advancements, laying the foundation for modern Western thought.
Events and important happenings are often tied to significant figures like Plato, whose life and work are reconstructed through historical calculations and other historical records.

• Ancient history challenges us to use indirect evidence to determine events and dates.
• It involves synthesizing information from various sources of the period.
• We often rely on the work of historians and archaeologists for these reconstructions.

arithmetical reasoning

Arithmetical reasoning involves the ability to understand and apply mathematical concepts to solve problems. It's not only about doing calculations, but about grasping what those calculations mean in context. For example, when determining Plato's birth year, simple subtraction was used. However, understanding how time was counted differently in the B.C. era also required logical reasoning.
Through arithmetical reasoning, students learn to apply logic to historical data, gaining insights into the context behind arithmetic operations. It's crucial in not just math, but in everyday decision-making, finance, and even historical analysis.

• It reinforces the importance of understanding context when solving problems.
• Helps in making informed conclusions based on numerical data.
• Encourages the recognition of patterns and structures in arithmetic operations.