The product of a positive number and the number that is 18 more than it is 703. What is the larger number?
Answer and explanation
Correct answer: 37
Let the positive number be \(x\). The other number is \(x+18\), so \(x(x+18)=703\), giving \(x^2+18x-703=0\). Factoring, \((x-19)(x+37)=0\), and the positive condition gives \(x=19\). Hence, the larger number is \(19+18=37\). Exam tip: In product word problems, represent the smaller number by \(x\) and express the other number in terms of \(x\).
Frequently asked questions
What is the correct answer to this question?
37
Why is this the correct answer?
Let the positive number be \(x\). The other number is \(x+18\), so \(x(x+18)=703\), giving \(x^2+18x-703=0\). Factoring, \((x-19)(x+37)=0\), and the positive condition gives \(x=19\). Hence, the larger number is \(19+18=37\). Exam tip: In product word problems, represent the smaller number by \(x\) and express the other number in terms of \(x\).
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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