In an examination, there are \(x\) students, and each student is given \((x-5)\) questions. If the total number of questions is \(414\), how many students are there?
Answer and explanation
Correct answer: 23
The total number of questions gives \(x(x-5)=414\). Thus, \(x^2-5x-414=0\), which factors as \((x-23)(x+18)=0\). Therefore, \(x=23\) or \(x=-18\). Since the number of students cannot be negative, the valid answer is \(23\). Exam tip: in word problems, reject algebraic roots that are impossible in the given context.
Frequently asked questions
What is the correct answer to this question?
23
Why is this the correct answer?
The total number of questions gives \(x(x-5)=414\). Thus, \(x^2-5x-414=0\), which factors as \((x-23)(x+18)=0\). Therefore, \(x=23\) or \(x=-18\). Since the number of students cannot be negative, the valid answer is \(23\). Exam tip: in word problems, reject algebraic roots that are impossible 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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