The product of two consecutive positive even numbers is 224. What is the smaller number?
Answer and explanation
Correct answer: 14
Let the smaller number be \(x\). The next consecutive even number is \(x+2\). Thus, \(x(x+2)=224\), giving \(x^2+2x-224=0\). Factoring gives \((x-14)(x+16)=0\), so \(x=14\) or \(x=-16\). Since the numbers are specified as positive, \(x=14\) is valid, and the numbers are 14 and 16. Exam tip: consecutive even numbers always differ by 2.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
Let the smaller number be \(x\). The next consecutive even number is \(x+2\). Thus, \(x(x+2)=224\), giving \(x^2+2x-224=0\). Factoring gives \((x-14)(x+16)=0\), so \(x=14\) or \(x=-16\). Since the numbers are specified as positive, \(x=14\) is valid, and the numbers are 14 and 16. Exam tip: consecutive even numbers always differ by 2.
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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