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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 Ishaan now?

Ishaan is \(2\) times as old as Christopher. \(35\) years ago, Ishaan was \(7\) times as old as Christopher.\newlineHow old is Ishaan 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 Ishaan now?
  1. Representation of Christopher's age: Let xx represent Christopher's current age. According to the problem, Ishaan is 22 times as old as Christopher, so Ishaan's current age is 2x2x.
  2. Ishaan's age 3535 years ago: 3535 years ago, Ishaan's age would have been 2x−352x - 35, and Christopher's age would have been x−35x - 35.
  3. Equation representing their ages: The problem states that egin{math}3535 ext{ years ago, Ishaan was }77 ext{ times as old as Christopher. We can write this as an equation: }22x - 3535 = 77(x - 3535). ext{}
  4. Solving the equation: Now we solve the equation for x. First, distribute the 77 on the right side of the equation: 2x−35=7x−2452x - 35 = 7x - 245.
  5. Calculating x: Next, we move all terms involving x to one side and constants to the other side: 2x−7x=−245+352x - 7x = -245 + 35.
  6. Calculating Christopher's current age: Simplify the equation: −5x=−210-5x = -210.
  7. Calculating Ishaan's current age: Divide both sides by −5 -5 to find x x : x=−210−5 x = \frac{-210}{-5}
  8. Calculating Ishaan's current age: Divide both sides by −5 -5 to find x x : x = \frac{\(-210\)}{\(-5\)} \.Calculate the value of \( x \: \( x = \(42 \.}
  9. Calculating Ishaan's current age: Divide both sides by −5 -5 to find x x : x=−210−5 x = \frac{-210}{-5} . Calculate the value of x $x=42 x \: \$ x = 42 . Now that we have Christopher's current age, we can find Ishaan's current age by multiplying Christopher's age by 2 Ishaan′sage=$2×42 2 \: Ishaan's age = \$ 2 \times 42
  10. Calculating Ishaan's current age: Divide both sides by −5-5 to find xx: x=−210−5x = \frac{-210}{-5}.Calculate the value of xx: x=42x = 42.Now that we have Christopher's current age, we can find Ishaan's current age by multiplying Christopher's age by 22: Ishaan's age = 2×422 \times 42.Calculate Ishaan's age: Ishaan's age = 8484.

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