A garden has \(x\) rows, with \((x+5)\) plants in each row. If there are 176 plants in total, how many rows are there?
Answer and explanation
Correct answer: 11
The total number of plants gives \(x(x+5)=176\), or \(x^2+5x-176=0\). Factoring, \((x-11)(x+16)=0\), so \(x=11\) or \(x=-16\). Since the number of rows cannot be negative, the answer is 11. Exam tip: In such application problems, retain only the positive root. Option 16 is incorrect because it uses the magnitude of the negative root \(-16\).
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
The total number of plants gives \(x(x+5)=176\), or \(x^2+5x-176=0\). Factoring, \((x-11)(x+16)=0\), so \(x=11\) or \(x=-16\). Since the number of rows cannot be negative, the answer is 11. Exam tip: In such application problems, retain only the positive root. Option 16 is incorrect because it uses the magnitude of the negative root \(-16\).
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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