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Finding the Third Proportional to 100,414 and 216,380

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Solution

The third proportional to 100,414 and 216,380 is: 466,272.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    100,414 : 216,380 = 216,380 : x
  2. Step 2: Convert to fraction form
    100,414/216,380 = 216,380/x
  3. Step 3: Cross multiply
    100,414x = 216,380 × 216,380
  4. Step 4: Simplify right side
    100,414x = 46,820,304,400
  5. Step 5: Solve for x
    x = 46,820,304,400/100,414
  6. Step 6: Final answer
    x = 466,272.68

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.