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Finding the Third Proportional to 232,978 and 509,573

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Solution

The third proportional to 232,978 and 509,573 is: 1,114,545.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    232,978 : 509,573 = 509,573 : x
  2. Step 2: Convert to fraction form
    232,978/509,573 = 509,573/x
  3. Step 3: Cross multiply
    232,978x = 509,573 × 509,573
  4. Step 4: Simplify right side
    232,978x = 259,664,642,329
  5. Step 5: Solve for x
    x = 259,664,642,329/232,978
  6. Step 6: Final answer
    x = 1,114,545.76

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.