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Ishaan is 2 times as old as Christopher. 35 years ago, Ishaan was 7 times as old as Christopher. How old is Christopher now?

Ishaan is \(2\) times as old as Christopher. \(35\) years ago, Ishaan was \(7\) times as old as Christopher.\newlineHow old is Christopher now?

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Full solution

Q. Ishaan is \(2\) times as old as Christopher. \(35\) years ago, Ishaan was \(7\) times as old as Christopher.\newlineHow old is Christopher now?
  1. Denoting Ages: Let's denote Christopher's current age as cc and Ishaan's current age as ii. According to the problem, Ishaan is 22 times as old as Christopher.\newlineFirst equation: i=2ci = 2c
  2. First Equation: 3535 years ago, Ishaan's age was i−35i - 35 and Christopher's age was c−35c - 35. According to the problem, at that time, Ishaan was 77 times as old as Christopher.\newlineSecond equation: i−35=7(c−35)i - 35 = 7(c - 35)
  3. Second Equation: Now we have a system of two equations:\newline11) i=2ci = 2c\newline22) i−35=7(c−35)i - 35 = 7(c - 35)\newlineWe can substitute the value of ii from the first equation into the second equation to find cc.
  4. Substituting ii into the Second Equation: Substituting i=2ci = 2c into the second equation:\newline2c−35=7(c−35)2c - 35 = 7(c - 35)\newlineExpanding the equation:\newline2c−35=7c−2452c - 35 = 7c - 245
  5. Expanding the Equation: Now, let's solve for cc:
    2c−7c=−245+352c - 7c = -245 + 35
    −5c=−210-5c = -210
    c=−210−5c = \frac{-210}{-5}
    c=42c = 42
  6. Solving for c: We found that Christopher's current age is 4242 years old. Now let's check if this satisfies the original conditions.\newlineIshaan's current age would be 2×42=842 \times 42 = 84 years old.\newline3535 years ago, Christopher was 42−35=742 - 35 = 7 years old, and Ishaan was 84−35=4984 - 35 = 49 years old.\newlineIndeed, 4949 is 77 times 77, so the conditions are satisfied.

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