A library has \(x\) shelves, and each shelf contains \(x+27\) books. If the total number of books is 1980, how many shelves are there?
Answer and explanation
Correct answer: 33
The total number of books gives the equation \(x(x+27)=1980\), or \(x^2+27x-1980=0\). Factoring gives \((x-33)(x+60)=0\), so \(x=33\) or \(x=-60\). Since the number of shelves cannot be negative, \(x=33\) is valid. Exam tip: In word problems, reject a negative root when the variable represents a count or measurement.
Frequently asked questions
What is the correct answer to this question?
33
Why is this the correct answer?
The total number of books gives the equation \(x(x+27)=1980\), or \(x^2+27x-1980=0\). Factoring gives \((x-33)(x+60)=0\), so \(x=33\) or \(x=-60\). Since the number of shelves cannot be negative, \(x=33\) is valid. Exam tip: In word problems, reject a negative root when the variable represents a count or measurement.
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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