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Finding the Third Proportional to 313,122 and 419,457

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Solution

The third proportional to 313,122 and 419,457 is: 561,902.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    313,122 : 419,457 = 419,457 : x
  2. Step 2: Convert to fraction form
    313,122/419,457 = 419,457/x
  3. Step 3: Cross multiply
    313,122x = 419,457 × 419,457
  4. Step 4: Simplify right side
    313,122x = 175,944,174,849
  5. Step 5: Solve for x
    x = 175,944,174,849/313,122
  6. Step 6: Final answer
    x = 561,902.95

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Why These Related Problems?

These problems maintain the same ratio (1.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.