In an examination, a total of 1600 question papers are distributed. If the number of students is \(x\) and each student receives \(x-18\) question papers, how many students are there?
Answer and explanation
Correct answer: 50
The total number of question papers gives \(x(x-18)=1600\). Thus, \(x^2-18x-1600=0\), which factors as \((x-50)(x+32)=0\). Therefore, \(x=50\) or \(x=-32\). Since the number of students cannot be negative, the valid answer is 50. Exam tip: reject any root that is not meaningful in the given context.
Frequently asked questions
What is the correct answer to this question?
50
Why is this the correct answer?
The total number of question papers gives \(x(x-18)=1600\). Thus, \(x^2-18x-1600=0\), which factors as \((x-50)(x+32)=0\). Therefore, \(x=50\) or \(x=-32\). Since the number of students cannot be negative, the valid answer is 50. Exam tip: reject any 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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