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Finding the Third Proportional to 102,784 and 219,140

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Solution

The third proportional to 102,784 and 219,140 is: 467,216.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,784 : 219,140 = 219,140 : x
  2. Step 2: Convert to fraction form
    102,784/219,140 = 219,140/x
  3. Step 3: Cross multiply
    102,784x = 219,140 × 219,140
  4. Step 4: Simplify right side
    102,784x = 48,022,339,600
  5. Step 5: Solve for x
    x = 48,022,339,600/102,784
  6. Step 6: Final answer
    x = 467,216.10

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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.