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Finding the Third Proportional to 419,430 and 586,458

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Solution

The third proportional to 419,430 and 586,458 is: 820,000.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    419,430 : 586,458 = 586,458 : x
  2. Step 2: Convert to fraction form
    419,430/586,458 = 586,458/x
  3. Step 3: Cross multiply
    419,430x = 586,458 × 586,458
  4. Step 4: Simplify right side
    419,430x = 343,932,985,764
  5. Step 5: Solve for x
    x = 343,932,985,764/419,430
  6. Step 6: Final answer
    x = 820,000.92

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.