Integers x and y satisfy 3 1/x * y 2/5 = 13 3/4 in lowest terms, where x = ? and y = ____________?
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Answer: D. x = 8, y = 4
Explanation
Converting mixed numbers into improper fractions simplifies algebraic expressions involving unknown variables. Equating the numerator and denominator products from both sides isolates the variables x and y. Solving the resulting system of equations yields the exact integer values x equals eight and y equals four. Mixed fractions combine whole numbers with fractional parts and must be converted for algebraic manipulation. Algebraic fraction equations require cross multiplication and factoring to determine unknown parameter values. Lowest terms simplification ensures that numerator and denominator share no common factors other than one.
Mathematical problem solving competitions use fraction and variable equations to test analytical reasoning skills. Engineering calculations convert mixed imperial units into improper fractions for precise computational modeling. Financial software algorithms process fractional equations when determining precise proportional interest distributions. Option A assigns an incorrect value to variable x while maintaining the correct y value. Option B provides incorrect values for both variables when tested against the original fraction equation. Option C fails to satisfy the numerator and denominator constraints established in the mixed fraction.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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