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Finding the Third Proportional to 82,970 and 178,246

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Solution

The third proportional to 82,970 and 178,246 is: 382,929.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,970 : 178,246 = 178,246 : x
  2. Step 2: Convert to fraction form
    82,970/178,246 = 178,246/x
  3. Step 3: Cross multiply
    82,970x = 178,246 × 178,246
  4. Step 4: Simplify right side
    82,970x = 31,771,636,516
  5. Step 5: Solve for x
    x = 31,771,636,516/82,970
  6. Step 6: Final answer
    x = 382,929.21

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.