Math Problem Statement

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

Solution

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+3k = d + 3 where kk is Kevin's age and dd is Daniel's age.

  2. Two years ago, Kevin was 4 times as old as Daniel: Two years ago, Kevin's age was k2k - 2, and Daniel's age was d2d - 2. According to the problem, Kevin was 4 times as old as Daniel at that time. This gives us the second equation: k2=4(d2)k - 2 = 4(d - 2)

Thus, the system of equations is:

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.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Systems of Equations

Formulas

k = d + 3
k - 2 = 4(d - 2)

Theorems

Basic properties of linear equations
Substitution method for solving systems of equations

Suitable Grade Level

Grades 6-8