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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 2020 years younger than Ishaan. Ishaan and Christopher first met two years ago. Fourteen years ago, Ishaan was 33 times as old as Christopher.\newlineHow old is Christopher now?\newline□ \square

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Full solution

Q. Christopher is 2020 years younger than Ishaan. Ishaan and Christopher first met two years ago. Fourteen years ago, Ishaan was 33 times as old as Christopher.\newlineHow old is Christopher now?\newline□ \square
  1. Define 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 equation:\newlineI=C+20I = C + 20
  2. Form Equations: We also know that they met two years ago, but this information does not provide a direct relationship between their ages at that time, so we will use the other piece of information provided. Fourteen years ago, Ishaan was 33 times as old as Christopher. We can write this as:\newlineI−14=3×(C−14)I - 14 = 3 \times (C - 14)
  3. Substitute and Simplify: Now we have a system of two equations:\newline11) I=C+20I = C + 20\newline22) I−14=3×(C−14)I - 14 = 3 \times (C - 14)\newlineWe can substitute the expression for II from the first equation into the second equation to solve for CC.\newline(C+20)−14=3×(C−14)(C + 20) - 14 = 3 \times (C - 14)
  4. Solve for C: Simplify the equation: C+6=3C−42C + 6 = 3C - 42
  5. Final Age Calculation: Now, we solve for CC: \newline3C−C=42+63C - C = 42 + 6\newline2C=482C = 48\newlineC=48/2C = 48 / 2\newlineC=24C = 24
  6. Final Age Calculation: Now, we solve for CC: \newline3C−C=42+63C - C = 42 + 6\newline2C=482C = 48\newlineC=482C = \frac{48}{2}\newlineC=24C = 24Christopher is currently 2424 years old.

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