In an age problem, the father's age is 36 years more than the son's age, and the product of their ages is 1980. What is the father's age?
Answer and explanation
Correct answer: 66 years
Let the son's age be \(x\) years. Then the father's age is \(x+36\) years. Therefore, \(x(x+36)=1980\), giving \(x^2+36x-1980=0\). Factoring yields \((x-30)(x+66)=0\). Since age cannot be negative, \(x=30\), so the father's age is \(30+36=66\) years. Exam tip: In age problems, reject any negative root of the quadratic equation.
Frequently asked questions
What is the correct answer to this question?
66 years
Why is this the correct answer?
Let the son's age be \(x\) years. Then the father's age is \(x+36\) years. Therefore, \(x(x+36)=1980\), giving \(x^2+36x-1980=0\). Factoring yields \((x-30)(x+66)=0\). Since age cannot be negative, \(x=30\), so the father's age is \(30+36=66\) years. Exam tip: In age problems, reject any negative root of the quadratic equation.
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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