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Finding the Third Proportional to 271,830 and 419,865

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Solution

The third proportional to 271,830 and 419,865 is: 648,517.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    271,830 : 419,865 = 419,865 : x
  2. Step 2: Convert to fraction form
    271,830/419,865 = 419,865/x
  3. Step 3: Cross multiply
    271,830x = 419,865 × 419,865
  4. Step 4: Simplify right side
    271,830x = 176,286,618,225
  5. Step 5: Solve for x
    x = 176,286,618,225/271,830
  6. Step 6: Final answer
    x = 648,517.89

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.