A fraction's denominator is 1 less than twice its numerator. Adding 1 to both numerator and denominator yields 3/5. Find the fraction.
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Answer: D. 5/9
Explanation
Letting the fraction be x over y, the denominator relationship is given by y equals two x minus one. Adding one to both numerator and denominator gives the new fraction equal to three-fifths, leading to the algebraic equation five x plus five equals three y plus three. Substituting y equals two x minus one into this equation yields x equals five and y equals nine, forming the fraction five-ninths. Fraction word problems are solved by translating descriptive numerator and denominator relationships into simultaneous linear equations. Algebraic substitution allows multi-variable fraction problems to be reduced to a single solvable variable. Checking the resulting fraction against all initial problem conditions ensures the mathematical solution is correct.
Option A fails to satisfy the denominator condition where y is one less than twice the numerator. Option B does not change to the required three-fifths ratio when one is added to both parts. Option C produces an incorrect ratio when subjected to the numerator and denominator addition steps.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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