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Ben is 39 years old and Ishaan is 3 years old.
How many years will it take until Ben is only 4 times as old as Ishaan?

Ben is \(39\) years old and Ishaan is \(3\) years old.\newlineHow many years will it take until Ben is only \(4\) times as old as Ishaan?

Full solution

Q. Ben is \(39\) years old and Ishaan is \(3\) years old.\newlineHow many years will it take until Ben is only \(4\) times as old as Ishaan?
  1. Denoting the number of years: Let's denote the number of years it will take for Ben to be only 44 times as old as Ishaan as nn. Currently, Ben is 3939 years old and Ishaan is 33 years old. After nn years, Ben will be 39+n39 + n years old and Ishaan will be 3+n3 + n years old. The equation to represent the situation where Ben is 44 times as old as Ishaan is:\newline39+n=4(3+n)39 + n = 4(3 + n)
  2. Distributing the 44 on the right side: Now, let's distribute the 44 on the right side of the equation:\newline39+n=12+4n39 + n = 12 + 4n
  3. Rearranging the equation to solve for n: Next, we will rearrange the equation to solve for "n". Let's subtract "n" from both sides of the equation:\newline39+nn=12+4nn39 + n - n = 12 + 4n - n\newline39=12+3n39 = 12 + 3n
  4. Isolating the term with n: Now, we will subtract 1212 from both sides to isolate the term with "n":\newline3912=12+3n1239 - 12 = 12 + 3n - 12\newline27=3n27 = 3n
  5. Dividing both sides to solve for n n : Finally, we will divide both sides by 3 3 to solve for n n :
    273=3n3 \frac{27}{3} = \frac{3n}{3}
    9=n 9 = n

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