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Ben is 4 times as old as Ishaan and is also 6 years older than Ishaan. How old is Ben?

Ben is \(4\) times as old as Ishaan and is also \(6\) years older than Ishaan.\newlineHow old is Ben?

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Full solution

Q. Ben is \(4\) times as old as Ishaan and is also \(6\) years older than Ishaan.\newlineHow old is Ben?
  1. Denoting Ben's and Ishaan's ages: Let's denote Ben's age as BB and Ishaan's age as II. According to the problem, Ben is 44 times as old as Ishaan. We can write this as an equation:\newlineB=4IB = 4I
  2. Equation 11: Ben is 44 times as old as Ishaan: The problem also states that Ben is 66 years older than Ishaan. We can write this as another equation:\newlineB=I+6B = I + 6
  3. Equation 22: Ben is 66 years older than Ishaan: Now we have a system of two equations with two variables:\newline11) B=4IB = 4I\newline22) B=I+6B = I + 6\newlineWe can solve this system by setting the two expressions for BB equal to each other since they both represent Ben's age.\newline4I=I+64I = I + 6
  4. System of equations: To find Ishaan's age, we need to solve for II. We can do this by subtracting II from both sides of the equation:\newline4I−I=I+6−I4I - I = I + 6 - I\newline3I=63I = 6
  5. Setting the expressions for Ben's age equal: Now we divide both sides by 33 to isolate I:\newline3I3=63\frac{3I}{3} = \frac{6}{3}\newlineI=2I = 2
  6. Solving for Ishaan's age: Now that we have Ishaan's age, we can find Ben's age by substituting II into one of the original equations. Let's use B=4IB = 4I:
    B=4×2B = 4 \times 2
    B=8B = 8

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