How Old is the Mother Now? Solving an Equation Using Algebra

Math challenges can sometimes feel like a puzzle waiting to be solved. In this article, we'll delve into a classic age problem, explore the solution step-by-step, and understand how algebra can be used to solve such puzzles easily. The problem at hand is as follows:

“A mother is 3 times as old as her son. In five years, their total age will be 50 years. How old is the mother now?”

The Problem Statement

Let’s break down the problem statement. First, we know that the mother is 3 times as old as her son. This relationship can be expressed as:

[ M 3S ]

Here, M represents the current age of the mother, and S represents the current age of the son.

Using Equations to Represent Future Ages

In five years, their ages will be:

[ M 5 ]

for the mother and

[ S 5 ]

for the son. According to the problem, their combined ages in five years will be 50:

[ (M 5) (S 5) 50 ]

Simplifying and Solving the Equation

Substitute the relationship (M 3S) into the equation:

[ (3S 5) (S 5) 50 ]

Simplify it further:

[ 4S 10 50 ]

Subtract 10 from both sides:

[ 4S 40 ]

Divide by 4:

[ S 10 ]

Now that we know the son’s current age, we can find the mother’s age:

[ M 3S 3 times 10 30 ]

Conclusion

The mother is currently 30 years old.

Verifying the Solution

To ensure our solution is correct, let’s plug the values back into the equation:

[ (M 5) (S 5) 50 ]

Substitute (M 30) and (S 10):

[ (30 5) (10 5) 35 15 50 ]

This verifies that our solution is accurate.

Additional Insight

This problem showcases the power of algebra to solve real-world problems. By representing the problem with equations and solving them step-by-step, we can arrive at a precise and verifiable answer. Algebra provides a structured approach to problem-solving in mathematics and helps in breaking down complex problems into manageable parts.

Bonus Problem

Now, consider another similar problem for additional practice:

“A father is twice as old as his daughter. In five years, their total age will be 72. How old is the father now?”

Solve this problem using a similar approach to the one we used for the mother and son.

Further Study

For more practice and to deepen your understanding, you can explore more age-related problems in algebra. These types of problems enhance analytical thinking and provide a foundation for more advanced mathematical concepts. Make sure to check your results and ensure consistency in your solutions.