In an assembly, there are \(x\) rows, and each row has \((x+10)\) chairs. If there are 416 chairs in total, how many rows are there?
Answer and explanation
Correct answer: 16
The total number of chairs gives \(x(x+10)=416\), or \(x^2+10x-416=0\). Factoring, \((x-16)(x+26)=0\), so \(x=16\) or \(x=-26\). Since the number of rows cannot be negative, the valid answer is 16. In such word problems, always check whether the root is meaningful in context.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The total number of chairs gives \(x(x+10)=416\), or \(x^2+10x-416=0\). Factoring, \((x-16)(x+26)=0\), so \(x=16\) or \(x=-26\). Since the number of rows cannot be negative, the valid answer is 16. In such word problems, always check whether the root is meaningful in 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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