The product of two consecutive positive integers is \(306\). What is the larger integer?
Answer and explanation
Correct answer: 18
Let the smaller integer be \(x\). Then the larger integer is \(x+1\), so \(x(x+1)=306\), or \(x^2+x-306=0\). Factoring gives \((x-17)(x+18)=0\). Since the integers are positive, \(x=17\), and the larger integer is \(x+1=18\). Therefore, 18 is correct. Exam tip: For consecutive integers, represent them as \(x\) and \(x+1\) before forming the quadratic equation.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
Let the smaller integer be \(x\). Then the larger integer is \(x+1\), so \(x(x+1)=306\), or \(x^2+x-306=0\). Factoring gives \((x-17)(x+18)=0\). Since the integers are positive, \(x=17\), and the larger integer is \(x+1=18\). Therefore, 18 is correct. Exam tip: For consecutive integers, represent them as \(x\) and \(x+1\) before forming the quadratic equation.
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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