When Will Abebe Be Exactly Twice as Old as Aster?

Abebe, a 12-year-old boy, has a younger sister named Aster who is two years old. The question is: in how many years will Abebe be exactly twice as old as Aster?

Setting Up the Problem

Let's denote the number of years from now as x. Currently, Abebe is 12 years old and Aster is 2 years old. In x years, their ages will be:

Abebe's age: 12 x Aster's age: 2 x

Solving the Equation

We want to find when Abebe will be exactly twice as old as Aster. So we set up the equation:

12 x 2(2 x)

Expanding and Rearranging the Equation

Expanding the equation:

12 x 4 2x

Now, we need to isolate x by moving terms involving x to one side of the equation and constant terms to the other:

12 - 4 2x - x

This simplifies to:

8 x

Verification

We can verify our solution by checking the ages in 8 years:

Abebe's age in 8 years: 12 8 20 Aster's age in 8 years: 2 8 10

Indeed, 20 is twice 10, confirming that the solution is correct.

Additional Problems for Reference

Sara and Her Brother's Age Problem:

Premises: Sara is 12 years old and her brother is 2 years old. Premises: Let Y be the number of years from now that Sara will be exactly twice as old as her brother. Mathematical Equation: 2(2 Y) 12 Y Solution: Y 8

Mathematical Problem Involving Sara and Her Brother:

Premises: Sara is 12 years old, and her brother is 2 years old. Premises: Let Y denote the time in years required for Sara to be exactly twice as old as her brother. Mathematical Equation: 2(2 Y) 12 Y Solution: Y 8

Conclusion

Whether it's about Abebe and Aster or Sara and her brother, the principle is the same. By setting up and solving a simple algebraic equation, we can determine how many years it will take for one person to be exactly twice as old as another.

These kinds of problems not only help in understanding basic algebra but are also a fun way to practice and challenge your logic and problem-solving skills. If you have a similar problem or question, feel free to reach out for assistance.