The sum of two numbers is 64 and their difference is 18. What is the smaller number?
Answer and explanation
Correct answer: 23
This is a word problem involving a pair of simultaneous linear equations. Let the larger number be x and the smaller number be y. Then x+y=64 and x−y=18. Adding these equations gives 2x=82, so x=41. Subtracting the second equation from the first gives 2y=46, or directly y=64−41=23. Therefore the smaller number is 23, so option C is correct. A quick check confirms both conditions: 41+23=64 and 41−23=18. Options A, B, and D fail at least one condition; for example, 24 would require the larger number to be 40, whose difference from 24 is only 16.
Frequently asked questions
What is the correct answer to this question?
23
Why is this the correct answer?
This is a word problem involving a pair of simultaneous linear equations. Let the larger number be x and the smaller number be y. Then x+y=64 and x−y=18. Adding these equations gives 2x=82, so x=41. Subtracting the second equation from the first gives 2y=46, or directly y=64−41=23. Therefore the smaller number is 23, so option C is correct. A quick check confirms both conditions: 41+23=64 and 41−23=18. Options A, B, and D fail at least one condition; for example, 24 would require the larger number to be 40, whose difference from 24 is only 16.
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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