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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 Kevin now?

Kevin is \(3\) times as old as Daniel. \(4\) years ago, Kevin was \(5\) times as old as Daniel.\newlineHow old is Kevin 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 Kevin now?
  1. Define Ages: Let's denote Kevin's current age as KK and Daniel's current age as DD. According to the problem, Kevin is 33 times as old as Daniel, which gives us the equation:\newlineK=3DK = 3D
  2. Equation 11: The problem also states that 44 years ago, Kevin was 55 times as old as Daniel. We can represent their ages 44 years ago as K−4K - 4 for Kevin and D−4D - 4 for Daniel. The equation based on this information is:\newlineK−4=5(D−4)K - 4 = 5(D - 4)
  3. Equation 22: Now we will expand the equation from the previous step to solve for DD:K−4=5D−20K - 4 = 5D - 20
  4. Expand Equation: Since we know from the first step that K=3DK = 3D, we can substitute 3D3D for KK in the equation:\newline3D−4=5D−203D - 4 = 5D - 20
  5. Substitute K: Next, we will solve for DD. To do this, we will move all terms involving DD to one side and the constant terms to the other side:\newline3D−5D=−20+43D - 5D = -20 + 4
  6. Solve for D: Simplifying the equation gives us:\newline−2D=−16-2D = -16
  7. Finalize D: Dividing both sides of the equation by −2-2 to solve for DD gives us:\newlineD=−16/−2D = -16 / -2\newlineD=8D = 8\newlineSo, Daniel is currently 88 years old.
  8. Find Kevin's Age: Now that we know Daniel's age, we can find Kevin's age by using the first equation K=3DK = 3D: \newlineK=3×8K = 3 \times 8\newlineK=24K = 24\newlineTherefore, Kevin is currently 2424 years old.

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