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Finding the Third Proportional to 102,565 and 221,533

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Solution

The third proportional to 102,565 and 221,533 is: 478,495.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,565 : 221,533 = 221,533 : x
  2. Step 2: Convert to fraction form
    102,565/221,533 = 221,533/x
  3. Step 3: Cross multiply
    102,565x = 221,533 × 221,533
  4. Step 4: Simplify right side
    102,565x = 49,076,870,089
  5. Step 5: Solve for x
    x = 49,076,870,089/102,565
  6. Step 6: Final answer
    x = 478,495.30

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.