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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 Ishaan 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 Ishaan 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 Ishaan now?
  1. Denoting Ishaan and Christopher's ages: Let's denote Ishaan's current age as II and Christopher's current age as CC. 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 represent 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 use substitution or elimination to solve this system. Let's use substitution since we already have II expressed in terms of CC from the first equation.
  4. Substitution method: Substitute the expression for II from the first equation into the second equation:\newline(C+20)−14=3(C−14)(C + 20) - 14 = 3(C - 14)\newlineNow, let's solve for CC.
  5. Solving for C: Simplify the equation:\newlineC+6=3C−42C + 6 = 3C - 42\newlineNow, let's isolate CC.
  6. Isolating C: Subtract C from both sides:\newline6=2C−426 = 2C - 42\newlineAdd 4242 to both sides:\newline48=2C48 = 2C\newlineNow, divide by 22 to find C.
  7. Finding Christopher's age: C=482C = \frac{48}{2}\newlineC=24C = 24\newlineChristopher is currently 2424 years old.
  8. Finding Ishaan's age: Now that we know Christopher's age, we can find Ishaan's current age using the first equation:\newlineI=C+20I = C + 20\newlineI=24+20I = 24 + 20
  9. Finding Ishaan's age: Now that we know Christopher's age, we can find Ishaan's current age using the first equation:\newlineI=C+20I = C + 20\newlineI=24+20I = 24 + 20I=44I = 44\newlineIshaan is currently 4444 years old.

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