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Finding the Third Proportional to 42,713 and 102,013

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Solution

The third proportional to 42,713 and 102,013 is: 243,641.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    42,713 : 102,013 = 102,013 : x
  2. Step 2: Convert to fraction form
    42,713/102,013 = 102,013/x
  3. Step 3: Cross multiply
    42,713x = 102,013 × 102,013
  4. Step 4: Simplify right side
    42,713x = 10,406,652,169
  5. Step 5: Solve for x
    x = 10,406,652,169/42,713
  6. Step 6: Final answer
    x = 243,641.33

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Why These Related Problems?

These problems maintain the same ratio (2.39) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.