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

Kevin is \(3\) years older than Daniel. Two years ago, Kevin was \(4\) times as old as Daniel.\newlineHow old is Daniel now?

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Full solution

Q. Kevin is \(3\) years older than Daniel. Two years ago, Kevin was \(4\) times as old as Daniel.\newlineHow old is Daniel now?
  1. Equation 11: Kevin's age: Let's denote Kevin's current age as KK and Daniel's current age as DD. According to the problem, Kevin is 33 years older than Daniel, which gives us our first equation:\newlineK=D+3K = D + 3
  2. Equation 22: Kevin's age two years ago: The problem also states that two years ago, Kevin was 44 times as old as Daniel. Two years ago, Kevin's age would have been K−2K - 2 and Daniel's age would have been D−2D - 2. The second equation based on this information is:\newlineK−2=4×(D−2)K - 2 = 4 \times (D - 2)
  3. System of equations: Now we have a system of two equations:\newline11) K=D+3K = D + 3\newline22) K−2=4×(D−2)K - 2 = 4 \times (D - 2)\newlineWe can substitute the value of KK from the first equation into the second equation to solve for DD.\newline(D+3)−2=4×(D−2)(D + 3) - 2 = 4 \times (D - 2)
  4. Substituting K K into equation 22: Simplify the equation: D+1=4D−8 D + 1 = 4D - 8
  5. Simplifying the equation: Now, let's solve for DD by moving all terms involving DD to one side and the constant terms to the other side:\newlineD−4D=−8−1D - 4D = -8 - 1\newline−3D=−9-3D = -9
  6. Solving for D: Divide both sides by −3 -3 to find the value of D:D=−9−3D = \frac{-9}{-3}D=3D = 3
  7. Daniel's current age: Daniel is currently 33 years old.

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