A library has 1530 books in total. If the number of shelves is x and each shelf contains (x+21) books, how many shelves are there?
Answer and explanation
Correct answer: 30
The total-number condition gives \(x(x+21)=1530\), so \(x^2+21x-1530=0\). Factoring gives \((x-30)(x+51)=0\), hence \(x=30\) or \(x=-51\). Since the number of shelves cannot be negative, the valid answer is 30. 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?
30
Why is this the correct answer?
The total-number condition gives \(x(x+21)=1530\), so \(x^2+21x-1530=0\). Factoring gives \((x-30)(x+51)=0\), hence \(x=30\) or \(x=-51\). Since the number of shelves cannot be negative, the valid answer is 30. 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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