Ben is $12$ years older than Ishaan. Ben and Ishaan first met two years ago. Three years ago, Ben was $4$ times as old as Ishaan. $\newline$ How old is Ishaan now? $\newline$ $\square$

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Percent of change: find the original amount word problems

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Q. Ben is

12

years older than Ishaan. Ben and Ishaan first met two years ago. Three years ago, Ben was

4

times as old as Ishaan.

\newline

How old is Ishaan now?

\newline

\square

Define Ages: Let's call Ishaan's current age ' $I$ ' and Ben's current age ' $B$ '. We know that Ben is $12$ years older than Ishaan, so we can write the equation $B = I + 12$ .
Establish Equations: They met $2$ years ago, but that doesn't affect their age difference, so we can ignore that part for now.
Substitute and Simplify: Three years ago, Ben was $4$ times as old as Ishaan. So, we can write the equation $B - 3 = 4 \times (I - 3)$ .
Solve for I: Now we have two equations: $B = I + 12$ and $B - 3 = 4 \times (I - 3)$ . Let's substitute the first equation into the second to solve for I. So, $(I + 12) - 3 = 4 \times (I - 3)$ .
Calculate $I$ : Simplify the equation: $I + 9 = 4I - 12$ .
Calculate I: Simplify the equation: $I + 9 = 4I - 12$ . Now, let's solve for $I$ . Subtract $I$ from both sides to get $9 = 3I - 12$ .
Calculate I: Simplify the equation: $I + 9 = 4I - 12$ .Now, let's solve for I. Subtract $I$ from both sides to get $9 = 3I - 12$ .Add $12$ to both sides to get $21 = 3I$ .
Calculate I: Simplify the equation: $I + 9 = 4I - 12$ . Now, let's solve for I. Subtract $I$ from both sides to get $9 = 3I - 12$ . Add $12$ to both sides to get $21 = 3I$ . Divide both sides by $3$ to find $I$ . So, $I = 21 / 3$ .
Calculate I: Simplify the equation: $I + 9 = 4I - 12$ . Now, let's solve for $I$ . Subtract $I$ from both sides to get $9 = 3I - 12$ . Add $12$ to both sides to get $21 = 3I$ . Divide both sides by $3$ to find $I$ . So, $I = 21 / 3$ . Calculate $I$ . $I$ $0$ . So, Ishaan is $I$ $1$ years old now.