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Kevin is 3 times as old as Daniel. 4 years ago, Kevin was 5 times as old as Daniel. How old is Daniel now?

Kevin is \(3\) times as old as Daniel. \(4\) years ago, Kevin was \(5\) times as old as Daniel.\newlineHow old is Daniel now?

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Full solution

Q. Kevin is \(3\) times as old as Daniel. \(4\) years ago, Kevin was \(5\) times as old as Daniel.\newlineHow old is Daniel now?
  1. Denoting Kevin and Daniel: Let's denote Kevin's age as KK and Daniel's age as DD. According to the problem, Kevin is 33 times as old as Daniel. We can write this as an equation:\newlineK=3DK = 3D
  2. Equation 11: Kevin is 33 times Daniel: The problem also states that 44 years ago, Kevin was 55 times as old as Daniel. We can represent this with another equation:\newlineK−4=5(D−4)K - 4 = 5(D - 4)
  3. Equation 22: 44 years ago, Kevin was 55 times Daniel: Now we have a system of two equations:\newline11) K=3DK = 3D\newline22) K−4=5(D−4)K - 4 = 5(D - 4)\newlineWe can use the first equation to substitute KK in the second equation.
  4. Substituting KK in Equation 22: Substituting KK from the first equation into the second equation gives us:\newline3D−4=5(D−4)3D - 4 = 5(D - 4)\newlineNow we will solve for DD.
  5. Solving for D: Expanding the equation, we get:\newline3D−4=5D−203D - 4 = 5D - 20\newlineNow, we will move all terms involving D to one side and constants to the other side.
  6. Moving terms and constants: Subtracting 3D3D from both sides, we get:\newline−4=2D−20-4 = 2D - 20\newlineAdding 2020 to both sides gives us:\newline16=2D16 = 2D
  7. Solving for D: Dividing both sides by 22 to solve for DD, we get:\newlineD=8D = 8\newlineSo, Daniel is 88 years old now.

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