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Finding the Third Proportional to 523,413 and 785,097

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Solution

The third proportional to 523,413 and 785,097 is: 1,177,611.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    523,413 : 785,097 = 785,097 : x
  2. Step 2: Convert to fraction form
    523,413/785,097 = 785,097/x
  3. Step 3: Cross multiply
    523,413x = 785,097 × 785,097
  4. Step 4: Simplify right side
    523,413x = 616,377,299,409
  5. Step 5: Solve for x
    x = 616,377,299,409/523,413
  6. Step 6: Final answer
    x = 1,177,611.75

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.