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Finding the Third Proportional to 416,821 and 645,824

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Solution

The third proportional to 416,821 and 645,824 is: 1,000,642.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    416,821 : 645,824 = 645,824 : x
  2. Step 2: Convert to fraction form
    416,821/645,824 = 645,824/x
  3. Step 3: Cross multiply
    416,821x = 645,824 × 645,824
  4. Step 4: Simplify right side
    416,821x = 417,088,638,976
  5. Step 5: Solve for x
    x = 417,088,638,976/416,821
  6. Step 6: Final answer
    x = 1,000,642.10

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.