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Kevin is 4 times as old as Daniel and is also 6 years older than Daniel.
How old is Kevin?

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

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Solve a system of equations using any method: word problems

Full solution

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

\newline

How old is Kevin?

Equation $1$ : Kevin's age in terms of Daniel's age: Let's denote Kevin's age as $K$ and Daniel's age as $D$ . According to the problem, Kevin is $4$ times as old as Daniel. We can write this as an equation: $\newline$ $K = 4D$
Equation $2$ : Kevin's age in terms of Daniel's age and age difference: The problem also states that Kevin is $6$ years older than Daniel. We can write this as another equation: $\newline$ $K = D + 6$
System of Equations: Now we have a system of two equations: $\newline$ $1$ ) $K = 4D$ $\newline$ $2$ ) $K = D + 6$ $\newline$ We can set these two equations equal to each other since they both equal $K$ . $\newline$ $4D = D + 6$
Setting the Equations Equal: Next, we solve for $D$ by subtracting $D$ from both sides of the equation: $\newline$ $4D - D = D + 6 - D$ $\newline$ $3D = 6$
Solving for Daniel's Age: Now, we divide both sides by $3$ to find the value of D: $\newline$ $\frac{3D}{3} = \frac{6}{3}$ $\newline$ $D = 2$
Finding Kevin's Age: Since we have found that Daniel is $2$ years old, we can now find Kevin's age by substituting $D$ back into one of the original equations. Let's use $K = 4D$ : $\newline$ $K = 4 \times 2$ $\newline$ $K = 8$

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