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Finding the Third Proportional to 102,456 and 209,970

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Solution

The third proportional to 102,456 and 209,970 is: 430,305.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,456 : 209,970 = 209,970 : x
  2. Step 2: Convert to fraction form
    102,456/209,970 = 209,970/x
  3. Step 3: Cross multiply
    102,456x = 209,970 × 209,970
  4. Step 4: Simplify right side
    102,456x = 44,087,400,900
  5. Step 5: Solve for x
    x = 44,087,400,900/102,456
  6. Step 6: Final answer
    x = 430,305.70

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.