Two numbers sum to 2490. If 6.5% of one equals 8.5% of the other, find the numbers:_________?
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Answer: D. 1411, 1079
Explanation
Letting the two numbers be x and y establishes their sum equation as x plus y equal to twenty-four ninety. Equating six point five percent of x to eight point five percent of y creates the simplified ratio thirteen x equal to seventeen y. Solving this simultaneous system of linear equations yields the exact number values of fourteen eleven and ten seventy-nine. Percentage equations convert directly into decimal or fractional multipliers to establish algebraic relationships between unknowns. Simultaneous linear equations allow mathematicians to determine multiple unknown values when provided with sufficient independent constraints. Systematic substitution or elimination methods provide robust pathways for solving complex multi-variable word problems.
Option A fails to sum to the required total of twenty-four ninety when added together. Option B does not satisfy the percentage equivalence condition where one percentage of x equals another percentage of y. Option C provides numbers that fail to maintain the correct proportion required by the percentage terms.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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