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Finding the Third Proportional to 82,176 and 193,920

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Solution

The third proportional to 82,176 and 193,920 is: 457,614.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,176 : 193,920 = 193,920 : x
  2. Step 2: Convert to fraction form
    82,176/193,920 = 193,920/x
  3. Step 3: Cross multiply
    82,176x = 193,920 × 193,920
  4. Step 4: Simplify right side
    82,176x = 37,604,966,400
  5. Step 5: Solve for x
    x = 37,604,966,400/82,176
  6. Step 6: Final answer
    x = 457,614.95

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Why These Related Problems?

These problems maintain the same ratio (2.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.