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Finding the Third Proportional to 102,319 and 209,557

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Solution

The third proportional to 102,319 and 209,557 is: 429,188.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,319 : 209,557 = 209,557 : x
  2. Step 2: Convert to fraction form
    102,319/209,557 = 209,557/x
  3. Step 3: Cross multiply
    102,319x = 209,557 × 209,557
  4. Step 4: Simplify right side
    102,319x = 43,914,136,249
  5. Step 5: Solve for x
    x = 43,914,136,249/102,319
  6. Step 6: Final answer
    x = 429,188.48

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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.