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A person's present age is \(x\) years. The product of the person's age after 7 years and the age 7 years ago is 1551. What is the person's present age?
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Answer and explanation
Correct answer: 40 years
The equation is \((x+7)(x-7)=1551\). Using the difference of squares, \(x^2-49=1551\), so \(x^2=1600\) and \(x=\pm 40\). Since age cannot be negative, the present age is 40 years. Exam tip: apply \((x+a)(x-a)=x^2-a^2\) directly in such age problems.
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What is the correct answer to this question?
40 years
Why is this the correct answer?
The equation is \((x+7)(x-7)=1551\). Using the difference of squares, \(x^2-49=1551\), so \(x^2=1600\) and \(x=\pm 40\). Since age cannot be negative, the present age is 40 years. Exam tip: apply \((x+a)(x-a)=x^2-a^2\) directly in such age problems.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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