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Finding the Third Proportional to 83,283 and 178,464

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Solution

The third proportional to 83,283 and 178,464 is: 382,423.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,283 : 178,464 = 178,464 : x
  2. Step 2: Convert to fraction form
    83,283/178,464 = 178,464/x
  3. Step 3: Cross multiply
    83,283x = 178,464 × 178,464
  4. Step 4: Simplify right side
    83,283x = 31,849,399,296
  5. Step 5: Solve for x
    x = 31,849,399,296/83,283
  6. Step 6: Final answer
    x = 382,423.78

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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.