A student solves 11 more questions each day than the number of days he studies. If he studies for x days and solves 900 questions in total, what is the value of x?
Answer and explanation
Correct answer: 25
The total number of questions gives the equation \(x(x+11)=900\), or \(x^2+11x-900=0\). Factoring gives \((x-25)(x+36)=0\), so \(x=25\) or \(x=-36\). Since the number of days cannot be negative, \(x=25\) is correct. In such word problems, always reject roots that are not meaningful in the given context.
Frequently asked questions
What is the correct answer to this question?
25
Why is this the correct answer?
The total number of questions gives the equation \(x(x+11)=900\), or \(x^2+11x-900=0\). Factoring gives \((x-25)(x+36)=0\), so \(x=25\) or \(x=-36\). Since the number of days cannot be negative, \(x=25\) is correct. In such word problems, always reject roots that are 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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