The sum of two numbers is 31 and their product is 238. What is the larger number?
Answer and explanation
Correct answer: 17
Let one number be \(x\); then the other number is \(31-x\). Thus, \(x(31-x)=238\), which gives \(x^2-31x+238=0\). Factoring, \((x-14)(x-17)=0\), so the two numbers are 14 and 17, and the larger number is 17. Exam tip: When the sum and product are given, look for a pair of numbers satisfying both conditions; the larger member of the pair is the answer.
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
Let one number be \(x\); then the other number is \(31-x\). Thus, \(x(31-x)=238\), which gives \(x^2-31x+238=0\). Factoring, \((x-14)(x-17)=0\), so the two numbers are 14 and 17, and the larger number is 17. Exam tip: When the sum and product are given, look for a pair of numbers satisfying both conditions; the larger member of the pair is the 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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