The product of two positive numbers is 216, and the larger number is 6 more than the smaller number. Find the smaller number.
Answer and explanation
Correct answer: 12
Let the smaller number be \(x\). Then the larger number is \(x+6\). Thus, \(x(x+6)=216\), giving \(x^2+6x-216=0\). Factoring, \((x-12)(x+18)=0\), so \(x=12\) or \(x=-18\). Since the numbers are positive, \(-18\) is rejected. Therefore, the smaller number is 12. Exam tip: In word problems involving positive numbers, discard any negative root.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
Let the smaller number be \(x\). Then the larger number is \(x+6\). Thus, \(x(x+6)=216\), giving \(x^2+6x-216=0\). Factoring, \((x-12)(x+18)=0\), so \(x=12\) or \(x=-18\). Since the numbers are positive, \(-18\) is rejected. Therefore, the smaller number is 12. Exam tip: In word problems involving positive numbers, discard any negative root.
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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