In a classroom, the number of rows is \(x\). Each row contains 3 more students than the number of rows. If there are 154 students in total, how many rows are there?
Answer and explanation
Correct answer: 11
If the number of rows is \(x\), then each row has \(x+3\) students. Thus, \(x(x+3)=154\), giving \(x^2+3x-154=0\). Factoring, \((x+14)(x-11)=0\), so \(x=11\) or \(x=-14\). Since the number of rows cannot be negative, the valid answer is 11. In such word problems, always reject a root that is not meaningful in the given context.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
If the number of rows is \(x\), then each row has \(x+3\) students. Thus, \(x(x+3)=154\), giving \(x^2+3x-154=0\). Factoring, \((x+14)(x-11)=0\), so \(x=11\) or \(x=-14\). Since the number of rows cannot be negative, the valid answer is 11. In such word problems, always reject a 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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