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Finding the Third Proportional to 105,434 and 232,464

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Solution

The third proportional to 105,434 and 232,464 is: 512,543.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    105,434 : 232,464 = 232,464 : x
  2. Step 2: Convert to fraction form
    105,434/232,464 = 232,464/x
  3. Step 3: Cross multiply
    105,434x = 232,464 × 232,464
  4. Step 4: Simplify right side
    105,434x = 54,039,511,296
  5. Step 5: Solve for x
    x = 54,039,511,296/105,434
  6. Step 6: Final answer
    x = 512,543.50

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.