Understanding the Age Word Problem

This problem involves determining Subhash's current age based on a future age relationship and then calculating when he will reach another age milestone relative to his current age. We need to set up algebraic equations to solve this.

Step 1: Define Variables

Let Subhash's current age be represented by the variable \(x\).

Step 2: Set Up Equation from the First Condition

The first condition states, "In 8 years, Subhash will be 3 times as old as he is now."

• Subhash's age in 8 years will be his current age plus 8, which is \(x + 8\).
• 3 times his current age is \(3 \times x\), or \(3x\).

So, the equation is:

\(x + 8 = 3x\)

Step 3: Solve for Subhash's Current Age

Now, we solve the equation from Step 2 to find the value of \(x\).

\(x + 8 = 3x\)

Subtract \(x\) from both sides:

\(8 = 3x - x\)

\(8 = 2x\)

Divide both sides by 2:

\(x = \frac{8}{2}\)

\(x = 4\)

So, Subhash's current age is 4 years.

Step 4: Set Up Equation for the Second Condition

The second question asks, "After how many years will Subhash be 5 times as old as he is now?"

Let \(y\) be the number of years after which Subhash will be 5 times his current age.

• Subhash's age after \(y\) years will be his current age plus \(y\), which is \(4 + y\).
• 5 times his current age is \(5 \times 4\), which is 20.

So, the equation is:

\(4 + y = 20\)

Step 5: Solve for the Number of Years

Now, we solve the equation from Step 4 to find the value of \(y\).

\(4 + y = 20\)

Subtract 4 from both sides:

\(y = 20 - 4\)

\(y = 16\)

Thus, after 16 years, Subhash will be 5 times as old as he is now.

Verification of the Solution

Let's check if our calculated current age and future age satisfy the conditions:

• Current age: 4 years
• In 8 years: Age will be \(4 + 8 = 12\) years. Is this 3 times the current age? \(3 \times 4 = 12\). Yes, it is.
• After 16 years: Age will be \(4 + 16 = 20\) years. Is this 5 times the current age? \(5 \times 4 = 20\). Yes, it is.

The calculations are consistent with the problem statements.

Summary of Steps

After 16 years, Subhash will be 5 times his current age of 4 years.

Revision Table: Understanding Age Problems

Additional Information: Solving Age Word Problems

Age word problems are common in algebra and involve relationships between people's ages at different points in time. Here are some tips for solving them:

• Always define your variable clearly, usually representing the current age of one or more people.
• Carefully read the problem to understand the relationship between the ages (e.g., "twice as old," "5 years older," "half the age," "in 10 years," "5 years ago").
• Translate each condition given in the problem into an algebraic equation. Remember that "in \(n\) years" means adding \(n\) to the current age, and " \(n\) years ago" means subtracting \(n\) from the current age.
• If there are multiple people, define variables for each person's current age or express one person's age in terms of another's.
• Solve the equation(s) to find the value(s) of the variable(s).
• Finally, make sure to answer the specific question asked in the problem, which might be the current age, a future age, or the number of years required.
• Always check your answer by plugging the values back into the original problem statement to see if the conditions are satisfied.