In an assembly, there are x rows, with (x+23) chairs in each row. If there are 1674 chairs in total, how many rows are there?
Answer and explanation
Correct answer: 31
The total-chair condition gives \(x(x+23)=1674\). Thus, \(x^2+23x-1674=0\), which factors as \((x-31)(x+54)=0\). Therefore, \(x=31\) or \(x=-54\). Since the number of rows cannot be negative, the valid answer is 31. Exam tip: In arrangement problems, express the total as ‘number of rows × items in each row’.
Frequently asked questions
What is the correct answer to this question?
31
Why is this the correct answer?
The total-chair condition gives \(x(x+23)=1674\). Thus, \(x^2+23x-1674=0\), which factors as \((x-31)(x+54)=0\). Therefore, \(x=31\) or \(x=-54\). Since the number of rows cannot be negative, the valid answer is 31. Exam tip: In arrangement problems, express the total as ‘number of rows × items in each row’.
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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