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Finding the Third Proportional to 102,032 and 216,414

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Solution

The third proportional to 102,032 and 216,414 is: 459,022.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,032 : 216,414 = 216,414 : x
  2. Step 2: Convert to fraction form
    102,032/216,414 = 216,414/x
  3. Step 3: Cross multiply
    102,032x = 216,414 × 216,414
  4. Step 4: Simplify right side
    102,032x = 46,835,019,396
  5. Step 5: Solve for x
    x = 46,835,019,396/102,032
  6. Step 6: Final answer
    x = 459,022.85

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.