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Finding the Third Proportional to 405,882 and 646,411

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Solution

The third proportional to 405,882 and 646,411 is: 1,029,479.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    405,882 : 646,411 = 646,411 : x
  2. Step 2: Convert to fraction form
    405,882/646,411 = 646,411/x
  3. Step 3: Cross multiply
    405,882x = 646,411 × 646,411
  4. Step 4: Simplify right side
    405,882x = 417,847,180,921
  5. Step 5: Solve for x
    x = 417,847,180,921/405,882
  6. Step 6: Final answer
    x = 1,029,479.46

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.