Solving Age Word Problems: Finding Surya's Age

This problem involves figuring out the current ages of Surya and his son based on the given information and then calculating Surya's age in the future. We can solve this by setting up algebraic equations.

Step-by-Step Solution for the Age Problem

Let's define variables for their current ages:

• Let Surya's current age be \(S\) years.
• Let his son's current age be \(Y\) years.

Now, we translate the given information into equations:

Information 1: Surya is 25 years older than his son.

This can be written as an equation:

\(S = Y + 25 \quad (Equation\ 1)\)

Information 2: In 5 years, he will be twice as old as his son.

First, let's find their ages in 5 years:

• Surya's age in 5 years will be \(S + 5\).
• Son's age in 5 years will be \(Y + 5\).

Solving the System of Equations

Now we have two equations with two variables:

\(Equation\ 1:\ S = Y + 25\)

\(Equation\ 2:\ S = 2Y + 5\)

Since both equations are equal to \(S\), we can set them equal to each other to solve for \(Y\):

\(Y + 25 = 2Y + 5\)

Now, solve for \(Y\):

Subtract \(Y\) from both sides:

\(25 = 2Y - Y + 5\)

\(25 = Y + 5\)

Subtract 5 from both sides:

\(25 - 5 = Y\)

\(20 = Y\)

So, the son's current age (\(Y\)) is 20 years.

Now substitute the value of \(Y\) (20) back into Equation 1 to find Surya's current age (\(S\)):

\(S = Y + 25\)

\(S = 20 + 25\)

\(S = 45\)

So, Surya's current age (\(S\)) is 45 years.

Calculating Surya's Age After 3 Years

The question asks for Surya's age after 3 years. His current age is 45 years.

Surya's age after 3 years = Current age + 3 years

Surya's age after 3 years = \(45 + 3\)

Surya's age after 3 years = \(48\)

Therefore, Surya will be 48 years old after 3 years.

Verification

Let's check if these ages satisfy the conditions:

• Current ages: Surya = 45, Son = 20. Is Surya 25 years older than his son? \(45 - 20 = 25\). Yes.
• Ages in 5 years: Surya = \(45 + 5 = 50\), Son = \(20 + 5 = 25\). Will Surya be twice as old as his son? \(50 = 2 \times 25\). Yes.

The calculated ages satisfy both conditions.

Revision Table: Key Concepts in Solving Age Problems

Additional Information: Solving Age Problems with Algebra

Age problems are common types of word problems in algebra. They typically involve finding the current ages of people based on information about their relative ages at different points in time (past, present, or future). The key to solving these problems is careful translation of the word statements into algebraic equations.

• Always define your variables clearly.
• Pay close attention to phrases like "older than," "younger than," "times as old," "in \(x\) years," or "\(x\) years ago."
• "Older than" or "younger than" usually translates to addition or subtraction.
• "Times as old" translates to multiplication.
• "In \(x\) years" means adding \(x\) to the current age.
• "\(x\) years ago" means subtracting \(x\) from the current age.
• If there are two variables, you will usually need at least two independent equations to solve the problem.
• After finding the current ages, make sure to answer the specific question asked, which might be an age in the future or past.

Practicing different types of age problems helps in understanding how to set up the equations correctly.