Ben is 30 years old and Daniel is 2 years old. How many years will it take until Ben is only 3 times as old as Daniel?

Denoting the years: Let's denote the number of years it will take for Ben to be only 3 times as old as Daniel by ＂n＂. Currently, Ben is 30 years old and Daniel is 2 years old. After ＂n＂ years, Ben will be 30 + n years old and Daniel will be 2 + n years old. We are looking for the value of ＂n＂ when Ben's age is 3 times Daniel's age. The equation to represent this situation is: 30 + n = 3(2 + n).Solving the equation: Now we will solve the equation for ＂n＂. First, distribute the 3 on the right side of the equation. 30 + n = 3 * 2 + 3 * n 30 + n = 6 + 3nRearranging the equation: Next, we will rearrange the equation to isolate ＂n＂ on one side. We can do this by subtracting ＂n＂ from both sides and also subtracting 6 from both sides. 30 + n - n - 6 = 6 + 3n - n - 6 24 = 2nDividing both sides: Now, we divide both sides by 2 to solve for ＂n＂. 24 / 2 = 2n / 2 12 = nFinal result: We have found that ＂n＂ equals 12. This means it will take 12 years for Ben to be only 3 times as old as Daniel.

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Ben is 30 years old and Daniel is 2 years old.
How many years will it take until Ben is only 3 times as old as Daniel?

Ben is $30$ years old and Daniel is $2$ years old. $\newline$ How many years will it take until Ben is only $3$ times as old as Daniel?

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Algebra 2

Solve a system of equations using any method: word problems

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Q. Ben is $30$ years old and Daniel is $2$ years old.

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How many years will it take until Ben is only $3$ times as old as Daniel?

Denoting the years: Let's denote the number of years it will take for Ben to be only $3$ times as old as Daniel by $n$ . Currently, Ben is $30$ years old and Daniel is $2$ years old. After $n$ years, Ben will be $30 + n$ years old and Daniel will be $2 + n$ years old. We are looking for the value of $n$ when Ben's age is $3$ times Daniel's age. $\newline$ The equation to represent this situation is: $30 + n = 3(2 + n)$ .
Solving the equation: Now we will solve the equation for ＂n＂. First, distribute the $3$ on the right side of the equation. $\newline$ $30 + n = 3 \times 2 + 3 \times n$ $\newline$ $30 + n = 6 + 3n$
Rearranging the equation: Next, we will rearrange the equation to isolate $n$ on one side. We can do this by subtracting $n$ from both sides and also subtracting $6$ from both sides. $\newline$ $30 + n - n - 6 = 6 + 3n - n - 6$ $\newline$ $24 = 2n$
Dividing both sides: Now, we divide both sides by $2$ to solve for $n$ . $\newline$ $\frac{24}{2} = \frac{2n}{2}$ $\newline$ $12 = n$
Final result: We have found that $n$ equals $12$ . This means it will take $12$ years for Ben to be only $3$ times as old as Daniel.