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Finding the Third Proportional to 232,460 and 509,138

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Solution

The third proportional to 232,460 and 509,138 is: 1,115,123.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    232,460 : 509,138 = 509,138 : x
  2. Step 2: Convert to fraction form
    232,460/509,138 = 509,138/x
  3. Step 3: Cross multiply
    232,460x = 509,138 × 509,138
  4. Step 4: Simplify right side
    232,460x = 259,221,503,044
  5. Step 5: Solve for x
    x = 259,221,503,044/232,460
  6. Step 6: Final answer
    x = 1,115,123.05

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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.