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Finding the Third Proportional to 232,949 and 509,517

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Solution

The third proportional to 232,949 and 509,517 is: 1,114,439.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    232,949 : 509,517 = 509,517 : x
  2. Step 2: Convert to fraction form
    232,949/509,517 = 509,517/x
  3. Step 3: Cross multiply
    232,949x = 509,517 × 509,517
  4. Step 4: Simplify right side
    232,949x = 259,607,573,289
  5. Step 5: Solve for x
    x = 259,607,573,289/232,949
  6. Step 6: Final answer
    x = 1,114,439.53

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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.