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Finding the Third Proportional to 311,961 and 463,353

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Solution

The third proportional to 311,961 and 463,353 is: 688,214.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    311,961 : 463,353 = 463,353 : x
  2. Step 2: Convert to fraction form
    311,961/463,353 = 463,353/x
  3. Step 3: Cross multiply
    311,961x = 463,353 × 463,353
  4. Step 4: Simplify right side
    311,961x = 214,696,002,609
  5. Step 5: Solve for x
    x = 214,696,002,609/311,961
  6. Step 6: Final answer
    x = 688,214.24

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.