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Finding the Third Proportional to 416,823 and 645,827

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Solution

The third proportional to 416,823 and 645,827 is: 1,000,646.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    416,823 : 645,827 = 645,827 : x
  2. Step 2: Convert to fraction form
    416,823/645,827 = 645,827/x
  3. Step 3: Cross multiply
    416,823x = 645,827 × 645,827
  4. Step 4: Simplify right side
    416,823x = 417,092,513,929
  5. Step 5: Solve for x
    x = 417,092,513,929/416,823
  6. Step 6: Final answer
    x = 1,000,646.59

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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.