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Finding the Third Proportional to 77,102 and 178,480

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Solution

The third proportional to 77,102 and 178,480 is: 413,155.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    77,102 : 178,480 = 178,480 : x
  2. Step 2: Convert to fraction form
    77,102/178,480 = 178,480/x
  3. Step 3: Cross multiply
    77,102x = 178,480 × 178,480
  4. Step 4: Simplify right side
    77,102x = 31,855,110,400
  5. Step 5: Solve for x
    x = 31,855,110,400/77,102
  6. Step 6: Final answer
    x = 413,155.44

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Why These Related Problems?

These problems maintain the same ratio (2.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.