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Finding the Third Proportional to 430,057 and 683,221

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Solution

The third proportional to 430,057 and 683,221 is: 1,085,416.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    430,057 : 683,221 = 683,221 : x
  2. Step 2: Convert to fraction form
    430,057/683,221 = 683,221/x
  3. Step 3: Cross multiply
    430,057x = 683,221 × 683,221
  4. Step 4: Simplify right side
    430,057x = 466,790,934,841
  5. Step 5: Solve for x
    x = 466,790,934,841/430,057
  6. Step 6: Final answer
    x = 1,085,416.43

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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.