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Finding the Third Proportional to 83,378 and 178,420

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Solution

The third proportional to 83,378 and 178,420 is: 381,799.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,378 : 178,420 = 178,420 : x
  2. Step 2: Convert to fraction form
    83,378/178,420 = 178,420/x
  3. Step 3: Cross multiply
    83,378x = 178,420 × 178,420
  4. Step 4: Simplify right side
    83,378x = 31,833,696,400
  5. Step 5: Solve for x
    x = 31,833,696,400/83,378
  6. Step 6: Final answer
    x = 381,799.71

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.