A library has 682 books in total. If the number of shelves is \(x\) and each shelf contains \(x+9\) books, how many shelves are there?
Answer and explanation
Correct answer: 22
The total number of books gives the equation \(x(x+9)=682\). Thus, \(x^2+9x-682=0\), which factors as \((x-22)(x+31)=0\). Hence, \(x=22\) or \(x=-31\). Since the number of shelves cannot be negative, the valid answer is 22. Exam tip: In word problems, retain only the positive root that fits the real-life context.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
The total number of books gives the equation \(x(x+9)=682\). Thus, \(x^2+9x-682=0\), which factors as \((x-22)(x+31)=0\). Hence, \(x=22\) or \(x=-31\). Since the number of shelves cannot be negative, the valid answer is 22. Exam tip: In word problems, retain only the positive root that fits the real-life context.
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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