Solving Age-related Word Problems Using Algebra

Word problems involving age can often be solved using basic algebraic equations. Let's explore a specific example where Sarah's age is twice that of her youngest brother, and the difference in their ages is 15 years. This problem can be solved using algebraic manipulation to find both Sarah's and her brother's ages.

Understanding the Problem

The problem states:

Let S represent Sarah's age. Let B represent her youngest brother's age. Sarah is twice as old as her youngest brother: ( S 2B ). The age difference between Sarah and her youngest brother is 15 years: ( S - B 15 ).

Solving the Equations

To solve for the ages, we start with the second piece of information, the age difference:

[ S - B 15 ]

Since we know from the first piece of information that Sarah's age is twice her brother's age, we can substitute ( S 2B ) into the age difference equation:

[ 2B - B 15 ]

Simplifying the equation:

[ B 15 ]

Therefore, the youngest brother is 15 years old.

Finding Sarah's Age

Now that we know the brother's age, we can find Sarah's age by substituting ( B 15 ) back into the equation ( S 2B ):

[ S 2 times 15 30 ]

So, Sarah is 30 years old.

Conclusion

To summarize, the youngest brother is 15 years old and Sarah is 30 years old. The problem was solved using a straightforward approach involving algebraic equations and substitutions.

Additional Tips for Solving Age Problems

Always define variables clearly. Translate the word problem into algebraic equations. Use substitution to solve for unknown values. Verify your solution by plugging the values back into the original equations.

These steps can be applied to a wide range of similar age problems, making algebra a powerful tool in mathematical problem-solving.