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Finding the Third Proportional to 408,140 and 643,512

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Solution

The third proportional to 408,140 and 643,512 is: 1,014,621.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    408,140 : 643,512 = 643,512 : x
  2. Step 2: Convert to fraction form
    408,140/643,512 = 643,512/x
  3. Step 3: Cross multiply
    408,140x = 643,512 × 643,512
  4. Step 4: Simplify right side
    408,140x = 414,107,694,144
  5. Step 5: Solve for x
    x = 414,107,694,144/408,140
  6. Step 6: Final answer
    x = 1,014,621.68

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.