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Finding the Third Proportional to 421,038 and 464,710

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Solution

The third proportional to 421,038 and 464,710 is: 512,911.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    421,038 : 464,710 = 464,710 : x
  2. Step 2: Convert to fraction form
    421,038/464,710 = 464,710/x
  3. Step 3: Cross multiply
    421,038x = 464,710 × 464,710
  4. Step 4: Simplify right side
    421,038x = 215,955,384,100
  5. Step 5: Solve for x
    x = 215,955,384,100/421,038
  6. Step 6: Final answer
    x = 512,911.86

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.