The plants in a garden are arranged in rows with an equal number of plants in each row. If the number of rows is \(x\) and each row contains \(x-6\) plants, there are 667 plants in total. How many rows are there?
Answer and explanation
Correct answer: 29
The total number of plants gives the equation \(x(x-6)=667\), or \(x^2-6x-667=0\). Factoring, \((x-29)(x+23)=0\), so \(x=29\) or \(x=-23\). Since the number of rows cannot be negative, \(x=29\) is the valid answer. Exam tip: In word problems, retain only the root that is meaningful in the given context.
Frequently asked questions
What is the correct answer to this question?
29
Why is this the correct answer?
The total number of plants gives the equation \(x(x-6)=667\), or \(x^2-6x-667=0\). Factoring, \((x-29)(x+23)=0\), so \(x=29\) or \(x=-23\). Since the number of rows cannot be negative, \(x=29\) is the valid answer. Exam tip: In word problems, retain only the root that is meaningful in the given 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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