In an examination, the number of students is \(x\), and each student is given \((x-11)\) questions. If the total number of questions given is \(1092\), how many students are there?
Answer and explanation
Correct answer: 39
The total number of questions gives \(x(x-11)=1092\). Thus, \(x^2-11x-1092=0\), which factors as \((x-39)(x+28)=0\). Therefore, \(x=39\) or \(x=-28\). Since the number of students cannot be negative, the valid answer is 39. Check: \(39\times(39-11)=39\times28=1092\). In such word problems, always reject a negative root when the variable represents a count.
Frequently asked questions
What is the correct answer to this question?
39
Why is this the correct answer?
The total number of questions gives \(x(x-11)=1092\). Thus, \(x^2-11x-1092=0\), which factors as \((x-39)(x+28)=0\). Therefore, \(x=39\) or \(x=-28\). Since the number of students cannot be negative, the valid answer is 39. Check: \(39\times(39-11)=39\times28=1092\). In such word problems, always reject a negative root when the variable represents a count.
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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