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Finding the Third Proportional to 82,034 and 120,747

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Solution

The third proportional to 82,034 and 120,747 is: 177,729.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,034 : 120,747 = 120,747 : x
  2. Step 2: Convert to fraction form
    82,034/120,747 = 120,747/x
  3. Step 3: Cross multiply
    82,034x = 120,747 × 120,747
  4. Step 4: Simplify right side
    82,034x = 14,579,838,009
  5. Step 5: Solve for x
    x = 14,579,838,009/82,034
  6. Step 6: Final answer
    x = 177,729.21

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.