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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 Kevin now?

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

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Q. Kevin is \(3\) years older than Daniel. Two years ago, Kevin was \(4\) times as old as Daniel.\newlineHow old is Kevin 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 use substitution or elimination to solve this system. Let's use substitution since we already have KK expressed in terms of DD from the first equation.
  4. Substitution method: Substitute KK from the first equation into the second equation:\newline(D+3)−2=4×(D−2)(D + 3) - 2 = 4 \times (D - 2)\newlineNow, let's solve for DD.
  5. Solving for D: Simplify the equation:\newlineD+1=4D−8D + 1 = 4D - 8\newlineNow, let's move all terms involving DD to one side and the constant terms to the other side.
  6. Simplifying the equation: Subtract DD from both sides and add 88 to both sides:\newlineD+1−D=4D−D−8+8D + 1 - D = 4D - D - 8 + 8\newline1=3D1 = 3D\newlineNow, divide both sides by 33 to solve for DD.
  7. Moving terms and constants: Dividing both sides by 33 gives us:\newlineD=13D = \frac{1}{3}\newlineThis is a math error because we expect DD to be a whole number since it represents an age. Let's go back and check our calculations.

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