When 4 is subtracted from a number and the result is multiplied by the same number, the product is 77. What is the positive number?
Answer and explanation
Correct answer: 11
Let the number be \(x\). According to the question, \(x(x-4)=77\), so \(x^2-4x-77=0\). Factoring gives \((x-11)(x+7)=0\), hence \(x=11\) or \(x=-7\). The positive number is 11; the close distractor 7 is incorrect because \(7(7-4)=21\), not 77. Exam tip: Translate the wording into a quadratic equation first, then select the solution that satisfies the stated condition.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
Let the number be \(x\). According to the question, \(x(x-4)=77\), so \(x^2-4x-77=0\). Factoring gives \((x-11)(x+7)=0\), hence \(x=11\) or \(x=-7\). The positive number is 11; the close distractor 7 is incorrect because \(7(7-4)=21\), not 77. Exam tip: Translate the wording into a quadratic equation first, then select the solution that satisfies the stated 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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