An assembly has \(x\) rows, with \((x+15)\) chairs in each row. If there are 1000 chairs in total, how many rows are there?
Answer and explanation
Correct answer: 25
The total-chair condition gives \(x(x+15)=1000\), so \(x^2+15x-1000=0\). Factoring, \((x-25)(x+40)=0\), which gives \(x=25\) or \(x=-40\). Since the number of rows cannot be negative, the valid answer is 25. In such word problems, always reject the negative root on the basis of the context.
Frequently asked questions
What is the correct answer to this question?
25
Why is this the correct answer?
The total-chair condition gives \(x(x+15)=1000\), so \(x^2+15x-1000=0\). Factoring, \((x-25)(x+40)=0\), which gives \(x=25\) or \(x=-40\). Since the number of rows cannot be negative, the valid answer is 25. In such word problems, always reject the negative root on the basis of the 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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