Quantities X, Y, and Z satisfy XY = kZ. Initially X = 4 and X:Y:Z = 2:3:4. If Y becomes 12 while Z stays constant, find X.
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Answer: A. 2
Explanation
Using the initial proportional ratio of 2 to 3 to 4 with X equal to 4 determines the scaling constant. Evaluating the relation XY equals kZ establishes the baseline constant for the given physical system. Adjusting Y to 12 while keeping Z constant requires X to decrease to 2 in order to maintain equality. Proportional ratios allow multi-variable quantities to be expressed using a shared scaling coefficient. Constant relationships in physics and algebra require balancing equations when one or more variables change. Inverse variation principles show that if the product of two variables remains constant, increasing one decreases the other.
Thermodynamics and fluid mechanics use governing equations where multiple physical properties maintain constant products. Economic supply and demand models analyze how changing one market factor forces adjustments in related variables. This problem tests advanced proportional reasoning and algebraic substitution skills across related quantities. Option B fails to satisfy the constant product relationship required between X, Y, and Z. Option C represents an incorrect calculation resulting from improper handling of the scaling constant. Option D ignores the inverse proportional adjustment needed when Y doubles in value.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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