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Ishaan is 3 times as old as Christopher and is also 14 years older than Christopher.
How old is Ishaan?

Ishaan is \(3\) times as old as Christopher and is also \(14\) years older than Christopher. $\newline$ How old is Ishaan?

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Solve a system of equations using any method: word problems

Full solution

Q. Ishaan is \(3\) times as old as Christopher and is also \(14\) years older than Christopher.

\newline

How old is Ishaan?

Equation $1$ : Ishaan's age in terms of Christopher's age: Let's denote Christopher's age as $c$ and Ishaan's age as $i$ . According to the problem, Ishaan is $3$ times as old as Christopher, which gives us the first equation: $\newline$ $i = 3c$
Equation $2$ : Ishaan's age in terms of Christopher's age and the age difference: The problem also states that Ishaan is $14$ years older than Christopher, which gives us the second equation: $\newline$ $i = c + 14$
System of Equations: Now we have a system of two equations: $\newline$ $1$ ) $i = 3c$ $\newline$ $2$ ) $i = c + 14$ $\newline$ We can set these two equations equal to each other since they both equal $i$ . $\newline$ $3c = c + 14$
Setting the Equations Equal: To find the value of $c$ , we will subtract $c$ from both sides of the equation: $\newline$ $3c - c = c + 14 - c$ $\newline$ $2c = 14$
Solving for Christopher's Age: Now we divide both sides by $2$ to solve for $c$ : $\frac{2c}{2} = \frac{14}{2}$ $c = 7$ Christopher is $7$ years old.
Finding Ishaan's Age: We can now use the value of c to find Ishaan's age using either of the original equations. Let's use the first equation $i = 3c$ : $i = 3 \times 7$ $i = 21$ Ishaan is $21$ years old.

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