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

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

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Solve a system of equations using any method: word problems

Full solution

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

\newline

How old is Ishaan?

Equation $1$ : Ben's age in terms of Ishaan's age: Let's denote Ishaan's age as ' $i$ ' and Ben's age as ' $b$ '. According to the problem, Ben is $4$ times as old as Ishaan, which gives us the first equation: $\newline$ $b = 4i$
Equation $2$ : Ben's age in terms of Ishaan's age and age difference: The problem also states that Ben is $6$ years older than Ishaan, which gives us the second equation: $\newline$ $b = i + 6$
System of Equations: Now we have a system of two equations with two variables: $\newline$ $1$ ) $b = 4i$ $\newline$ $2$ ) $b = i + 6$ $\newline$ We can solve this system by setting the two expressions for 'b' equal to each other since they both represent Ben's age. $\newline$ $4i = i + 6$
Setting the expressions for Ben's age equal: Subtract $i$ from both sides of the equation to solve for $i$ :
$4i - i = i + 6 - i$
$3i = 6$
Solving for Ishaan's age: Divide both sides of the equation by $3$ to find the value of 'i': $\newline$ $\frac{3i}{3} = \frac{6}{3}$ $\newline$ $i = 2$
Conclusion: Now that we have found the value of ' $i$ ', which represents Ishaan's age, we can conclude that Ishaan is $2$ years old.

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