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Finding the Third Proportional to 83,176 and 178,264

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Solution

The third proportional to 83,176 and 178,264 is: 382,057.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,176 : 178,264 = 178,264 : x
  2. Step 2: Convert to fraction form
    83,176/178,264 = 178,264/x
  3. Step 3: Cross multiply
    83,176x = 178,264 × 178,264
  4. Step 4: Simplify right side
    83,176x = 31,778,053,696
  5. Step 5: Solve for x
    x = 31,778,053,696/83,176
  6. Step 6: Final answer
    x = 382,057.97

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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.