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Finding the Third Proportional to 412,342 and 580,656

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Solution

The third proportional to 412,342 and 580,656 is: 817,674.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    412,342 : 580,656 = 580,656 : x
  2. Step 2: Convert to fraction form
    412,342/580,656 = 580,656/x
  3. Step 3: Cross multiply
    412,342x = 580,656 × 580,656
  4. Step 4: Simplify right side
    412,342x = 337,161,390,336
  5. Step 5: Solve for x
    x = 337,161,390,336/412,342
  6. Step 6: Final answer
    x = 817,674.14

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.