The product of the numbers that are 14 less than and 25 more than a positive number is 2700. What is the positive number?
Answer and explanation
Correct answer: 50
Let the positive number be x. Then \((x-14)(x+25)=2700\). On expanding and simplifying, \(x^2+11x-3050=0\), which factors as \((x-50)(x+61)=0\). Thus, \(x=50\) or \(x=-61\); since the number is specified as positive, the correct answer is 50. Exam tip: Always check the roots of a quadratic against the conditions stated in the word problem, such as positivity.
Frequently asked questions
What is the correct answer to this question?
50
Why is this the correct answer?
Let the positive number be x. Then \((x-14)(x+25)=2700\). On expanding and simplifying, \(x^2+11x-3050=0\), which factors as \((x-50)(x+61)=0\). Thus, \(x=50\) or \(x=-61\); since the number is specified as positive, the correct answer is 50. Exam tip: Always check the roots of a quadratic against the conditions stated in the word problem, such as positivity.
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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