Kevin is 3 years older than Daniel. Two years ago, Kevin was 4 times as old as Daniel.
Let k be Kevin's age and let d be Daniel's age. create a system of equations

Let's break down the problem step by step to create a system of equations.

1. **Kevin is 3 years older than Daniel:**
   This gives us the first equation:
   \[
   k = d + 3
   \]
   where \(k\) is Kevin's age and \(d\) is Daniel's age.

2. **Two years ago, Kevin was 4 times as old as Daniel:**
   Two years ago, Kevin's age was \(k - 2\), and Daniel's age was \(d - 2\). According to the problem, Kevin was 4 times as old as Daniel at that time. This gives us the second equation:
   \[
   k - 2 = 4(d - 2)
   \]

Thus, the system of equations is:
\[
\begin{cases}
k = d + 3 \\
k - 2 = 4(d - 2)
\end{cases}
\]

Do you want me to solve this system of equations for \(k\) and \(d\)?

Here are 5 related questions:
1. What will be Kevin and Daniel's ages in 5 years?
2. What was the difference in their ages 10 years ago?
3. If Kevin were 10 years older than Daniel, how would the equations change?
4. What happens if Kevin was twice Daniel's age two years ago instead of 4 times?
5. Can we generalize this problem for any age difference between Kevin and Daniel?

**Tip:** When creating systems of equations, it's important to carefully translate relationships and conditions described in the problem into algebraic terms.

Kevin is 3 years older than Daniel. Two years ago, Kevin was 4 times as old as Daniel. Let k be Kevin's age and let d be Daniel's age. Create a system of equations.

Learn how to solve a system of linear equations involving the ages of Kevin and Daniel. This problem uses algebra to set up two equations based on age differences and a proportional relationship from two years ago. Suitable for students in Grades 6-8.

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