The product of two positive numbers is 378, and the larger number is 3 more than the smaller number. Find the smaller number.
Answer and explanation
Correct answer: 18
Let the smaller number be \(x\). Then the larger number is \(x+3\). Thus, \(x(x+3)=378\), which gives \(x^2+3x-378=0\). Factoring, \((x-18)(x+21)=0\), so \(x=18\) or \(x=-21\). Since both numbers are positive, \(-21\) is rejected and the smaller number is 18. Exam tip: In word problems, always check the given condition, such as positivity, before accepting a quadratic root.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
Let the smaller number be \(x\). Then the larger number is \(x+3\). Thus, \(x(x+3)=378\), which gives \(x^2+3x-378=0\). Factoring, \((x-18)(x+21)=0\), so \(x=18\) or \(x=-21\). Since both numbers are positive, \(-21\) is rejected and the smaller number is 18. Exam tip: In word problems, always check the given condition, such as positivity, before accepting a quadratic 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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