The sum of two numbers is 15 and their product is 54. What is the larger number?
Answer and explanation
Correct answer: 9
Use the sum-and-product relationship for a quadratic equation. Let one number be y; then the other is 15 − y. Their product gives y(15 − y) = 54, so y² − 15y + 54 = 0. Factoring yields (y − 9)(y − 6) = 0, hence the two numbers are 9 and 6. The larger number is therefore 9. Substitution verifies both conditions: 9 + 6 = 15 and 9 × 6 = 54. Option B is the smaller number, not the requested larger one. Options C and D do not produce the required product with a partner having sum 15: 12 would pair with 3 and give product 36, while 15 would pair with 0 and give product 0.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
Use the sum-and-product relationship for a quadratic equation. Let one number be y; then the other is 15 − y. Their product gives y(15 − y) = 54, so y² − 15y + 54 = 0. Factoring yields (y − 9)(y − 6) = 0, hence the two numbers are 9 and 6. The larger number is therefore 9. Substitution verifies both conditions: 9 + 6 = 15 and 9 × 6 = 54. Option B is the smaller number, not the requested larger one. Options C and D do not produce the required product with a partner having sum 15: 12 would pair with 3 and give product 36, while 15 would pair with 0 and give product 0.
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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