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Finding the Third Proportional to 77,469 and 164,239

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Solution

The third proportional to 77,469 and 164,239 is: 348,196.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    77,469 : 164,239 = 164,239 : x
  2. Step 2: Convert to fraction form
    77,469/164,239 = 164,239/x
  3. Step 3: Cross multiply
    77,469x = 164,239 × 164,239
  4. Step 4: Simplify right side
    77,469x = 26,974,449,121
  5. Step 5: Solve for x
    x = 26,974,449,121/77,469
  6. Step 6: Final answer
    x = 348,196.69

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.