The product of a positive number and the number 4 more than it is 165. What is the number?
Answer and explanation
Correct answer: 11
Let the number be \(x\). The other number is \(x+4\), so \(x(x+4)=165\). Thus, \(x^2+4x-165=0\), which factors as \((x-11)(x+15)=0\). The roots are \(x=11\) and \(x=-15\), but the number is specified as positive; therefore, the correct answer is 11. Exam tip: “4 more than a number” means \(x+4\), not \(4x\).
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
Let the number be \(x\). The other number is \(x+4\), so \(x(x+4)=165\). Thus, \(x^2+4x-165=0\), which factors as \((x-11)(x+15)=0\). The roots are \(x=11\) and \(x=-15\), but the number is specified as positive; therefore, the correct answer is 11. Exam tip: “4 more than a number” means \(x+4\), not \(4x\).
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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