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Finding the Third Proportional to 384,114 and 509,706

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Solution

The third proportional to 384,114 and 509,706 is: 676,362.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    384,114 : 509,706 = 509,706 : x
  2. Step 2: Convert to fraction form
    384,114/509,706 = 509,706/x
  3. Step 3: Cross multiply
    384,114x = 509,706 × 509,706
  4. Step 4: Simplify right side
    384,114x = 259,800,206,436
  5. Step 5: Solve for x
    x = 259,800,206,436/384,114
  6. Step 6: Final answer
    x = 676,362.24

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.