The product of the larger of two positive numbers and the number that is 7 less than it is 198. What is the larger number?
Answer and explanation
Correct answer: 18
Let the larger number be \(x\). Then the other number is \(x-7\), so \(x(x-7)=198\). Thus, \(x^2-7x-198=0\), which factors as \((x-18)(x+11)=0\). The roots are \(x=18\) and \(x=-11\). Since the numbers are positive, the valid larger number is 18, and the other number is 11. Exam tip: In such problems, represent the larger number by \(x\) and the number 7 less than it by \(x-7\).
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
Let the larger number be \(x\). Then the other number is \(x-7\), so \(x(x-7)=198\). Thus, \(x^2-7x-198=0\), which factors as \((x-18)(x+11)=0\). The roots are \(x=18\) and \(x=-11\). Since the numbers are positive, the valid larger number is 18, and the other number is 11. Exam tip: In such problems, represent the larger number by \(x\) and the number 7 less than it by \(x-7\).
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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