Solving Age Problems in Mathematics: The Case of Sadia and Her Mother

Mathematics often involves solving practical and interesting problems, such as those related to ages. This article illustrates how to solve a specific problem involving the ages of Sadia and her mother using algebra and linear equations. We'll also discuss the importance of these techniques for Google SEO, ensuring that our content is easily discoverable by Google and other search engines.

Problem Statement

The sum of the ages of Sadia and her mother is 70 years. 10 years earlier, Sadia's age was a quarter of her mother’s age. What are the present ages of Sadia and her mother?

Setting Up the Equations

Let's denote Sadia's current age as S and her mother's current age as M.

From the problem statement, we get two key pieces of information:

The sum of their ages is 70: S M 70[/itex] 10 years earlier, Sadia's age was a quarter of her mother’s age: S - 10 14(M - 10)

Solving the Equations Step by Step

Let's solve these equations step by step.

Step 1: Rearrange the First Equation

From the first equation, we can express M in terms of S:

M 70 - S

Step 2: Substitute into the Second Equation

Now substitute M into the second equation:S - 10 14(70 - S - 10)

Step 3: Clear the Fraction

Multiply both sides by 4 to eliminate the fraction:

4(S - 10) 1(70 - S - 10)

4S - 40 60 - S

Step 4: Combine Like Terms

Add S to both sides:

4S S - 40 60

5S - 40 60

Add 40 to both sides:

5S 100

Divide both sides by 5:

S 20

Step 5: Find the Mother's Age

Now substitute S back into the equation for M:

M 70 - S 70 - 20 50

Conclusion

Sadia's mother is currently 50 years old.

Mathematics, particularly algebra and linear equations, is crucial for solving a wide range of problems, from real-life scenarios to complex theoretical issues. Understanding these concepts is essential for Google SEO as well. By structuring content to include relevant keywords, mathematical examples, and step-by-step problem-solving techniques, our articles become more informative and SEO-friendly.

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