A library has \(x\) racks, with \(x+6\) books in each rack. If the library has a total of \(391\) books, how many racks are there?
Answer and explanation
Correct answer: 17
The total number of books equals the number of racks multiplied by the books in each rack, so \(x(x+6)=391\). Thus, \(x^2+6x-391=0\), which factors as \((x-17)(x+23)=0\). The roots are \(x=17\) and \(x=-23\); since the number of racks cannot be negative, \(x=17\) is correct. Exam tip: In real-life word problems, reject a negative root when the variable represents a quantity.
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
The total number of books equals the number of racks multiplied by the books in each rack, so \(x(x+6)=391\). Thus, \(x^2+6x-391=0\), which factors as \((x-17)(x+23)=0\). The roots are \(x=17\) and \(x=-23\); since the number of racks cannot be negative, \(x=17\) is correct. Exam tip: In real-life word problems, reject a negative root when the variable represents a quantity.
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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