A number multiplied by the number (5) more than it gives (204). What is the number?
Answer and explanation
Correct answer: (12)
Let the unknown number be x. The number that is 5 greater than it is x + 5. Their product is given as 204, so the condition is x(x + 5) = 204. This creates a quadratic equation, and both algebraic roots should be considered before selecting the intended positive number.
Expanding gives x² + 5x − 204 = 0. Factoring, (x − 12)(x + 17) = 0, so x = 12 or x = −17. The positive number asked for in the choices is 12, and 12 × 17 = 204. Thus option A is correct. The negative root also satisfies the equation algebraically but is not listed as the intended answer.
Frequently asked questions
What is the correct answer to this question?
(12)
Why is this the correct answer?
Let the unknown number be x. The number that is 5 greater than it is x + 5. Their product is given as 204, so the condition is x(x + 5) = 204. This creates a quadratic equation, and both algebraic roots should be considered before selecting the intended positive number.
Expanding gives x² + 5x − 204 = 0. Factoring, (x − 12)(x + 17) = 0, so x = 12 or x = −17. The positive number asked for in the choices is 12, and 12 × 17 = 204. Thus option A is correct. The negative root also satisfies the equation algebraically but is not listed as the intended answer.
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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