A student solves \(x+22\) questions each day for \(x\) days, completing 1400 questions in total. What is the value of \(x\)?
Answer and explanation
Correct answer: 28
The total number of questions gives \(x(x+22)=1400\). Thus, \(x^2+22x-1400=0\), which factors as \((x-28)(x+50)=0\). Therefore, \(x=28\) or \(x=-50\); since the number of days cannot be negative, the valid answer is 28. 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?
28
Why is this the correct answer?
The total number of questions gives \(x(x+22)=1400\). Thus, \(x^2+22x-1400=0\), which factors as \((x-28)(x+50)=0\). Therefore, \(x=28\) or \(x=-50\); since the number of days cannot be negative, the valid answer is 28. 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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