A bus has \(x\) rows, with \(x-2\) seats in each row. If there are 224 seats in total, how many rows are there?
Answer and explanation
Correct answer: 16
The total-seat condition gives \(x(x-2)=224\). Thus, \(x^2-2x-224=0\), which factors as \((x-16)(x+14)=0\). Hence, \(x=16\) or \(x=-14\). Since the number of rows cannot be negative, the valid answer is 16. Exam tip: In word problems, always check the roots against the conditions of the real situation, such as being a positive integer.
Frequently asked questions
What is the correct answer to this question?
16
Why is this the correct answer?
The total-seat condition gives \(x(x-2)=224\). Thus, \(x^2-2x-224=0\), which factors as \((x-16)(x+14)=0\). Hence, \(x=16\) or \(x=-14\). Since the number of rows cannot be negative, the valid answer is 16. Exam tip: In word problems, always check the roots against the conditions of the real situation, such as being a positive integer.
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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