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Finding the Third Proportional to 82,407 and 176,478

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Solution

The third proportional to 82,407 and 176,478 is: 377,934.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,407 : 176,478 = 176,478 : x
  2. Step 2: Convert to fraction form
    82,407/176,478 = 176,478/x
  3. Step 3: Cross multiply
    82,407x = 176,478 × 176,478
  4. Step 4: Simplify right side
    82,407x = 31,144,484,484
  5. Step 5: Solve for x
    x = 31,144,484,484/82,407
  6. Step 6: Final answer
    x = 377,934.94

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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.