The product of the larger of two positive numbers and the number that is 10 less than it is 375. What is the larger number?
Answer and explanation
Correct answer: 25
Let the larger number be \(x\). The other number is then \(x-10\), so \(x(x-10)=375\). This gives \(x^2-10x-375=0\), or \((x-25)(x+15)=0\). Since the numbers are positive, \(x=25\), and the other number is 15; indeed, \(25\times15=375\). Therefore, option C is correct. Exam tip: Translate “10 less than a number” as \(x-10\), not \(10-x\).
Frequently asked questions
What is the correct answer to this question?
25
Why is this the correct answer?
Let the larger number be \(x\). The other number is then \(x-10\), so \(x(x-10)=375\). This gives \(x^2-10x-375=0\), or \((x-25)(x+15)=0\). Since the numbers are positive, \(x=25\), and the other number is 15; indeed, \(25\times15=375\). Therefore, option C is correct. Exam tip: Translate “10 less than a number” as \(x-10\), not \(10-x\).
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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