Solving the Age Puzzle: A System of Equations Approach

Imagine a group of four boys: Chris, John, Jim, and Sam. The relationships between their ages are given in the age puzzle provided. Let's explore how to systematically solve for the ages of each of these boys using a system of equations. Here's how we break it down step-by-step:

We start by defining variables for each boy's age:

Chris's age C John's age J Jim's age X Sam's age S

Based on the given relationships, we can write the following equations:

C J 4 J X 4 X S 4 S 0.5 * C

Let's solve these equations step-by-step. First, we substitute the value of S from the fourth equation into the third equation:

X 0.5 * C - 4

Next, we substitute X from this equation into the second equation:

J 0.5 * C - 4 4 J 0.5 * C

Now, we substitute J into the first equation:

C 0.5 * C 4

Let's solve for C:

C - 0.5 * C 4 0.5 * C 4 C 8 * 4 C 24

Now that we have Chris's age, we can find the other boys' ages:

John's age (J) 24 - 4 20 Jim's age (X) 20 - 4 16 Sam's age (S) 16 - 4 12

To verify, let's check the relationships given:

Chris is 24 years old, which is 4 years older than John (20). John is 20 years old, which is 4 years older than Jim (16). Jim is 16 years old, which is 4 years older than Sam (12). Sam is 12 years old, which is half the age of Chris (24).

Thus, the ages are confirmed to be correct. Here are the ages summarized:

Chris is 24 years old John is 20 years old Jim is 16 years old Sam is 12 years old

This method not only solves the puzzle but also demonstrates the power of setting up and solving a system of equations. Understanding how to systematically approach and solve such puzzles is valuable in various mathematical and real-world scenarios.

Keywords: Age puzzle, system of equations, solution