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Finding the Third Proportional to 83,640 and 180,412

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Solution

The third proportional to 83,640 and 180,412 is: 389,149.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,640 : 180,412 = 180,412 : x
  2. Step 2: Convert to fraction form
    83,640/180,412 = 180,412/x
  3. Step 3: Cross multiply
    83,640x = 180,412 × 180,412
  4. Step 4: Simplify right side
    83,640x = 32,548,489,744
  5. Step 5: Solve for x
    x = 32,548,489,744/83,640
  6. Step 6: Final answer
    x = 389,149.81

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.