The product of the numbers that are 9 less and 16 more than a number is 1650. What is the positive original number?
Answer and explanation
Correct answer: 39
Let the original number be \(x\). Then \((x-9)(x+16)=1650\), which gives \(x^2+7x-1650=0\), or \((x-39)(x+46)=0\). Thus, \(x=39\) or \(x=-46\); the positive original number is \(39\). In such questions, translate ‘9 less’ as \(x-9\) and ‘16 more’ as \(x+16\) before expanding.
Frequently asked questions
What is the correct answer to this question?
39
Why is this the correct answer?
Let the original number be \(x\). Then \((x-9)(x+16)=1650\), which gives \(x^2+7x-1650=0\), or \((x-39)(x+46)=0\). Thus, \(x=39\) or \(x=-46\); the positive original number is \(39\). In such questions, translate ‘9 less’ as \(x-9\) and ‘16 more’ as \(x+16\) before expanding.
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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