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Finding the Third Proportional to 54,823 and 82,013

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Solution

The third proportional to 54,823 and 82,013 is: 122,688.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    54,823 : 82,013 = 82,013 : x
  2. Step 2: Convert to fraction form
    54,823/82,013 = 82,013/x
  3. Step 3: Cross multiply
    54,823x = 82,013 × 82,013
  4. Step 4: Simplify right side
    54,823x = 6,726,132,169
  5. Step 5: Solve for x
    x = 6,726,132,169/54,823
  6. Step 6: Final answer
    x = 122,688.14

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.