In an assembly, there are (x) rows and each row has (x+12) chairs. There are (640) chairs in total. What is the number of rows?
Answer and explanation
Correct answer: (20)
If there are \(x\u0005 rows and each row contains \(x+12\u0005 chairs, the total number of chairs is their product. Thus \(x(x+12)=640\u0005. Expanding gives \(x^2+12x-640=0\u0005. This factors as \((x-20)(x+32)=0\u0005, so the algebraic values are \(x=20\u0005 and \(x=-32\u0005.
A number of rows cannot be negative, so only \(x=20\u0005 is meaningful. There are then 32 chairs per row, and \(20\times32=640\u0005 confirms the result. Therefore option B is correct. The negative root is rejected because it has no physical meaning in this counting situation.
Frequently asked questions
What is the correct answer to this question?
(20)
Why is this the correct answer?
If there are \(x\u0005 rows and each row contains \(x+12\u0005 chairs, the total number of chairs is their product. Thus \(x(x+12)=640\u0005. Expanding gives \(x^2+12x-640=0\u0005. This factors as \((x-20)(x+32)=0\u0005, so the algebraic values are \(x=20\u0005 and \(x=-32\u0005.
A number of rows cannot be negative, so only \(x=20\u0005 is meaningful. There are then 32 chairs per row, and \(20\times32=640\u0005 confirms the result. Therefore option B is correct. The negative root is rejected because it has no physical meaning in this counting situation.
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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