In an examination, if the number of correctly solved questions is \(x\), the marks obtained are \(x(20-x)\). If the marks obtained are 96, what is the larger possible value of \(x\)?
Answer and explanation
Correct answer: 12
From the given relation, \(x(20-x)=96\). Rearranging gives \(20x-x^2=96\), or \(x^2-20x+96=0\). Factoring, \((x-8)(x-12)=0\), so \(x=8\) or \(x=12\). Therefore, the larger value of \(x\) is 12. Exam tip: after finding both roots of a quadratic equation, select the larger or smaller one according to what the question asks.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
From the given relation, \(x(20-x)=96\). Rearranging gives \(20x-x^2=96\), or \(x^2-20x+96=0\). Factoring, \((x-8)(x-12)=0\), so \(x=8\) or \(x=12\). Therefore, the larger value of \(x\) is 12. Exam tip: after finding both roots of a quadratic equation, select the larger or smaller one according to what the question asks.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
