Two numbers are in a 5:9 ratio. Reducing each by 5 changes the ratio to 5:11. Find the numbers.
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Answer: D. 15, 27
Explanation
Representing the numbers as algebraic multiples allows setting up a fractional equation for reduction. Subtracting five from both terms and equating the result to five over eleven forms the correct expression. Solving the linear equation for the unknown variable reveals a multiplier value equal to three. Ratio problems can be solved by introducing a common variable multiplier for each proportional term. Linear equations derived from word problems require careful algebraic manipulation to isolate the unknown. Substituting the solved multiplier back into the original expressions yields the final numeric values.
Algebraic ratio adjustments are common in chemistry when calculating adjusted concentrations of liquid solutions. Financial analysts use proportional scaling to adjust budget allocations when expenses decrease uniformly. Educational assessments frequently test algebraic problem solving skills using similar multi step word problems. Option A gives thirty and nineteen which do not maintain the initial five to nine ratio. Option B provides twenty one and thirty seven which fail to satisfy the reduction conditions. Option C suggests fifteen and thirty four which yield an incorrect final reduced ratio value.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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