The sum of two numbers is (21) and their difference is (5). What is the larger number?
Answer and explanation
Correct answer: 13
Let the larger number be \(x\) and the smaller number be \(y\). Then \(x+y=21\) and \(x-y=5\). Adding the equations gives \(2x=26\), so \(x=13\). Therefore, the larger number is 13. If 14 were chosen, the other number would be 7 and their difference would be 7, not 5. Exam tip: In sum-and-difference questions, add the two equations to find the larger number directly.
Frequently asked questions
What is the correct answer to this question?
13
Why is this the correct answer?
Let the larger number be \(x\) and the smaller number be \(y\). Then \(x+y=21\) and \(x-y=5\). Adding the equations gives \(2x=26\), so \(x=13\). Therefore, the larger number is 13. If 14 were chosen, the other number would be 7 and their difference would be 7, not 5. Exam tip: In sum-and-difference questions, add the two equations to find the larger number directly.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Algebraic methods: Substitution method and Elimination method..
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