The product of the number that is 11 less than a number and the number that is 20 more than it is 2112. What is the positive original number?
Answer and explanation
Correct answer: 44
Let the original number be \(x\). Then \((x-11)(x+20)=2112\), which gives \(x^2+9x-2332=0\). Factoring, \((x-44)(x+53)=0\), so \(x=44\) or \(x=-53\). Since the question asks for the positive original number, the answer is 44. Exam tip: use a minus sign for ‘less than’ and a plus sign for ‘more than’, then apply the stated positivity condition.
Frequently asked questions
What is the correct answer to this question?
44
Why is this the correct answer?
Let the original number be \(x\). Then \((x-11)(x+20)=2112\), which gives \(x^2+9x-2332=0\). Factoring, \((x-44)(x+53)=0\), so \(x=44\) or \(x=-53\). Since the question asks for the positive original number, the answer is 44. Exam tip: use a minus sign for ‘less than’ and a plus sign for ‘more than’, then apply the stated positivity condition.
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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