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A person's present age is \(x\) years. The product of the person's age 5 years from now and age 5 years ago is 875. What is the person's present age?
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Answer and explanation
Correct answer: 30 years
From the condition, \((x+5)(x-5)=875\). Using the difference-of-squares identity gives \(x^2-25=875\), so \(x^2=900\) and \(x=\pm 30\). Since age cannot be negative, the present age is 30 years. In age problems, always reject the negative root.
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What is the correct answer to this question?
30 years
Why is this the correct answer?
From the condition, \((x+5)(x-5)=875\). Using the difference-of-squares identity gives \(x^2-25=875\), so \(x^2=900\) and \(x=\pm 30\). Since age cannot be negative, the present age is 30 years. In age problems, always reject the negative root.
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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