A library has \(x\) shelves, and each shelf contains \((x+13)\) books. If the library has 1014 books in total, how many shelves are there?
Answer and explanation
Correct answer: 26
The total number of books gives the equation \(x(x+13)=1014\). Thus, \(x^2+13x-1014=0\), which factors as \((x-26)(x+39)=0\). Hence, \(x=26\) or \(x=-39\). Since the number of shelves cannot be negative, \(x=26\) is correct. The value 39 represents the number of books per shelf when \(x=26\), not the number of shelves. Exam tip: In word problems, reject any algebraic root that is not meaningful in the given context.
Frequently asked questions
What is the correct answer to this question?
26
Why is this the correct answer?
The total number of books gives the equation \(x(x+13)=1014\). Thus, \(x^2+13x-1014=0\), which factors as \((x-26)(x+39)=0\). Hence, \(x=26\) or \(x=-39\). Since the number of shelves cannot be negative, \(x=26\) is correct. The value 39 represents the number of books per shelf when \(x=26\), not the number of shelves. Exam tip: In word problems, reject any algebraic root that is not meaningful in the given 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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