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Finding the Third Proportional to 213,684 and 455,970

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Solution

The third proportional to 213,684 and 455,970 is: 972,972.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    213,684 : 455,970 = 455,970 : x
  2. Step 2: Convert to fraction form
    213,684/455,970 = 455,970/x
  3. Step 3: Cross multiply
    213,684x = 455,970 × 455,970
  4. Step 4: Simplify right side
    213,684x = 207,908,640,900
  5. Step 5: Solve for x
    x = 207,908,640,900/213,684
  6. Step 6: Final answer
    x = 972,972.43

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.