Three consecutive odd numbers are arranged in ascending sequence such that the addition of the final two integers exceeds the first integer by 13. Determine these three numbers?
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Answer: D. 7, 9, 11
Explanation
Letting three consecutive odd numbers be represented as x minus two, x, and x plus two establishes their algebraic sequence. The sum of the final two numbers exceeds the first number by thirteen, yielding the equation x plus x plus two minus quantity x minus two equal to thirteen. Solving this linear equation gives x equals nine, making the three consecutive odd numbers seven, nine, and eleven. Consecutive odd numbers always maintain a fixed difference of two units between each successive integer in the sequence. Algebraic word problems translate descriptive English statements into mathematical equations to solve for unknown integer values. Linear equation simplification allows for rapid determination of sequence baselines when given comparative sum conditions.
Option A suggests nine, eleven, and thirteen, which yields a different sum comparison when tested against the problem rules. Option B proposes eleven, thirteen, and fifteen, failing to satisfy the thirteen-unit difference condition. Option C offers thirteen, fifteen, and seventeen, overestimating the required values for the sequence.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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