The sum of two numbers is 17 and their product is 72. What is the smaller number?
Answer and explanation
Correct answer: 8
This is a quadratic word problem based on the sum and product of two numbers. Let one number be x; then the other is 17 − x because their sum is 17. Using the product condition, x(17 − x) = 72. On rearranging, 17x − x² = 72, so x² − 17x + 72 = 0. Factoring gives (x − 8)(x − 9) = 0, so the two numbers are 8 and 9. Since the question asks for the smaller number, the answer is 8, which is option B. We can verify both conditions directly: 8 + 9 = 17 and 8 × 9 = 72. Option C is the larger number, while 6 and 12 do not satisfy both conditions because their sum is 18 and their product is 72.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
This is a quadratic word problem based on the sum and product of two numbers. Let one number be x; then the other is 17 − x because their sum is 17. Using the product condition, x(17 − x) = 72. On rearranging, 17x − x² = 72, so x² − 17x + 72 = 0. Factoring gives (x − 8)(x − 9) = 0, so the two numbers are 8 and 9. Since the question asks for the smaller number, the answer is 8, which is option B. We can verify both conditions directly: 8 + 9 = 17 and 8 × 9 = 72. Option C is the larger number, while 6 and 12 do not satisfy both conditions because their sum is 18 and their product is 72.
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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