Two figures maintain a 3 : 5 proportion. Deducting 9 from each yields new figures in a 12 : 23 proportion. Identify the smaller value :________?
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Answer: C. 49
Explanation
Representing the two initial figures as 3x and 5x allows subtraction of 9 from each to form a new ratio. Setting the resulting algebraic fraction equal to twelve over twenty-three permits solving for the variable x. Solving the equation yields an x value of 49, which correctly satisfies the secondary ratio condition. Proportional ratio problems use an unknown multiplier variable to represent the initial quantities accurately. Linear equations derived from ratios are solved by cross-multiplication and isolating the variable term. Checking solutions by substituting the derived variable back into the original ratio confirms mathematical validity.
Demographic studies use proportional shifts over time to model population changes in different age groups. Financial forecasting models adjust baseline asset ratios when fixed deductions are applied to accounts. This problem reinforces the technique of setting up and solving fractional equations from verbal descriptions. Option A represents an incorrect variable solution that fails to satisfy the reduced ratio condition. Option B results from an arithmetic error during the cross-multiplication and expansion of terms. Option D overestimates the required variable value needed to balance the subtraction ratio equation.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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