The product of the numbers that are respectively 8 and 15 more than a positive number is 2340. What is the original number?
Answer and explanation
Correct answer: 37
Let the original number be \(x\). Then \((x+8)(x+15)=2340\), which gives \(x^2+23x-2220=0\), or \((x-37)(x+60)=0\). Thus, \(x=37\) or \(x=-60\); since the number is specified as positive, the correct answer is 37. Exam tip: Always check both roots and select the one satisfying the condition stated in the question.
Frequently asked questions
What is the correct answer to this question?
37
Why is this the correct answer?
Let the original number be \(x\). Then \((x+8)(x+15)=2340\), which gives \(x^2+23x-2220=0\), or \((x-37)(x+60)=0\). Thus, \(x=37\) or \(x=-60\); since the number is specified as positive, the correct answer is 37. Exam tip: Always check both roots and select the one satisfying the condition stated in the question.
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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