Questions: Kevin is 3 years older than Daniel. Two years ago, Kevin was 4 times as old as Daniel. How old is Daniel now?

Transcript text: Kevin is 3 years older than Daniel. Two years ago, Kevin was 4 times as old as Daniel. How old is Daniel now?

Solution

Solution Steps

Step 1: Define Variables

Let \( K \) represent Kevin's current age and \( D \) represent Daniel's current age. According to the problem, Kevin is 3 years older than Daniel. Therefore, we can write the equation:

\[ K = D + 3 \]

Step 2: Set Up the Equation Based on Past Ages

The problem states that 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 \( D - 2 \). We can write the equation:

\[ K - 2 = 4(D - 2) \]

Step 3: Substitute and Solve

Substitute the expression for \( K \) from Step 1 into the equation from Step 2:

\[ (D + 3) - 2 = 4(D - 2) \]

Simplify the equation:

\[ D + 1 = 4D - 8 \]

Rearrange the terms to solve for \( D \):

\[ 1 + 8 = 4D - D \]

\[ 9 = 3D \]

Divide both sides by 3:

\[ D = 3 \]