In an age problem, the father's age is 42 years more than the son's age, and the product of their ages is 2160. What is the father's age?
Answer and explanation
Correct answer: 72 years
Let the son's age be \(x\) years. Then the father's age is \(x+42\) years, so \(x(x+42)=2160\). This gives \(x^2+42x-2160=0\), which factors as \((x-30)(x+72)=0\). Since age must be positive, \(x=30\), and the father's age is \(30+42=72\) years. Option 60 does not satisfy both the age difference and the product conditions. Exam tip: In age problems, reject the negative root and retain only the positive age.
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What is the correct answer to this question?
72 years
Why is this the correct answer?
Let the son's age be \(x\) years. Then the father's age is \(x+42\) years, so \(x(x+42)=2160\). This gives \(x^2+42x-2160=0\), which factors as \((x-30)(x+72)=0\). Since age must be positive, \(x=30\), and the father's age is \(30+42=72\) years. Option 60 does not satisfy both the age difference and the product conditions. Exam tip: In age problems, reject the negative root and retain only the positive age.
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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