How Old Is Your Brother If You Are 30 and He Is 90% of Your Age?

Have you ever come across a scenario where someone is 90% of your age and wondered how to calculate their actual age? This question often arises, especially among siblings or friends, and can be quite intriguing. Let's break it down with a clear example and a step-by-step explanation.

Understanding the Problem

The problem at hand is: If you are 30 years old and your brother is 90% of your age, how old is he?

Solving the Problem Using a Percentage Calculation

To solve this, follow these simple steps:

Identify the given information: You are 30 years old and your brother is 90% of your age. Convert the percentage to a decimal: 90% is equivalent to 0.90. Multiply your age by the decimal: 30 years * 0.90 27 years.

Therefore, your brother is 27 years old.

Mathematical Approach

For a more advanced understanding, let's solve this using an algebraic approach.

Using Algebra

Let x represent the age of your brother. The relationship between your age and your brother's age can be expressed as:

30 / x 100 / 90

Now, let's cross multiply:

30 * 90 100 * x

2700 10

x 2700 / 100

x 27

Hence, your brother is 27 years old.

Why the Mathematical Solution Works

The mathematical approach here involves setting up a proportion. If you are 30 years old and your brother is 90% of your age, the proportion of your age to your brother's age can be written as:

Age of brother / Your age 90 / 100

Using cross multiplication, we can solve for your brother's age:

Age of brother (90 / 100) * Your age

Substituting your age (30 years) into the equation:

Age of brother (90 / 100) * 30

Age of brother 27

Conclusion

From both the percentage calculation and the algebraic approach, we determined that if you are 30 years old and your brother is 90% of your age, he is 27 years old. This method can be applied to similar scenarios where ages are compared using percentages.

Remember, percentages and proportions offer a powerful tool for solving real-life problems. If you have any other age-related questions or similar calculations, this approach can be very helpful. Feel free to leave your thoughts or any questions in the comments below!