A classroom has \(x\) benches, with \((x-1)\) students sitting on each bench. If there are 72 students in total, how many benches are there?
Answer and explanation
Correct answer: 9
The total number of students gives \(x(x-1)=72\), or \(x^2-x-72=0\). Factoring, \((x-9)(x+8)=0\), so \(x=9\) or \(x=-8\). Since the number of benches cannot be negative, \(x=9\) is the valid answer. In word problems, remember to reject roots that have no practical meaning.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
The total number of students gives \(x(x-1)=72\), or \(x^2-x-72=0\). Factoring, \((x-9)(x+8)=0\), so \(x=9\) or \(x=-8\). Since the number of benches cannot be negative, \(x=9\) is the valid answer. In word problems, remember to reject roots that have no practical meaning.
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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