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Christopher is 20 years younger than Ishaan. Ishaan and Christopher first met two years ago. Fourteen years ago, Ishaan was 3 times as old as Christopher. How old is Christopher now?

Christopher is \(20\) years younger than Ishaan. Ishaan and Christopher first met two years ago. Fourteen years ago, Ishaan was \(3\) times as old as Christopher.\newlineHow old is Christopher now?

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Full solution

Q. Christopher is \(20\) years younger than Ishaan. Ishaan and Christopher first met two years ago. Fourteen years ago, Ishaan was \(3\) times as old as Christopher.\newlineHow old is Christopher now?
  1. Denoting Christopher and Ishaan's ages: Let's denote Christopher's current age as CC and Ishaan's current age as II. According to the problem, Christopher is 2020 years younger than Ishaan, which gives us the first equation:\newlineI=C+20I = C + 20
  2. Equation 11: I=C+20I = C + 20: The problem states that fourteen years ago, Ishaan was 33 times as old as Christopher. We can express their ages fourteen years ago as I−14I - 14 for Ishaan and C−14C - 14 for Christopher. The second equation based on this information is:\newlineI−14=3(C−14)I - 14 = 3(C - 14)
  3. Equation 22: I−14=3(C−14)I - 14 = 3(C - 14): Now we have a system of two equations:\newline11) I=C+20I = C + 20\newline22) I−14=3(C−14)I - 14 = 3(C - 14)\newlineWe can substitute the value of II from the first equation into the second equation to solve for CC.\newline(C+20)−14=3(C−14)(C + 20) - 14 = 3(C - 14)
  4. Substituting I I into Equation 22: Simplify the equation:\newlineC+20−14=3C−42 C + 20 - 14 = 3C - 42 \newlineC+6=3C−42 C + 6 = 3C - 42
  5. Simplifying the equation: Now, we will solve for CC by moving all terms involving CC to one side of the equation and constants to the other side:\newlineC−3C=−42−6C - 3C = -42 - 6\newline−2C=−48-2C = -48
  6. Solving for C: Divide both sides by −2 -2 to find the value of C:C=−48−2C = \frac{-48}{-2}C=24C = 24
  7. Checking the solution: Now that we have the value of CC, which represents Christopher's current age, we can check if it makes sense with the information given. If Christopher is 2424 now, then Ishaan is 24+20=4424 + 20 = 44 years old. Fourteen years ago, Christopher was 24−14=1024 - 14 = 10 years old, and Ishaan was 44−14=3044 - 14 = 30 years old. Indeed, 3030 is three times 1010, so our solution is consistent with the problem.

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