A garden has \(x\) rows, with \((x-16)\) plants in each row. If there are \(1536\) plants in total, how many rows are there?
Answer and explanation
Correct answer: 48
The total-number condition gives \(x(x-16)=1536\), so \(x^2-16x-1536=0\). Factoring yields \((x-48)(x+32)=0\), giving \(x=48\) or \(x=-32\). Since the number of rows cannot be negative, \(x=48\) is correct. Exam tip: In word problems, reject roots that are not meaningful for the given quantity.
Frequently asked questions
What is the correct answer to this question?
48
Why is this the correct answer?
The total-number condition gives \(x(x-16)=1536\), so \(x^2-16x-1536=0\). Factoring yields \((x-48)(x+32)=0\), giving \(x=48\) or \(x=-32\). Since the number of rows cannot be negative, \(x=48\) is correct. Exam tip: In word problems, reject roots that are not meaningful for the given quantity.
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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