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Finding the Third Proportional to 83,513 and 96,689

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Solution

The third proportional to 83,513 and 96,689 is: 111,943.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,513 : 96,689 = 96,689 : x
  2. Step 2: Convert to fraction form
    83,513/96,689 = 96,689/x
  3. Step 3: Cross multiply
    83,513x = 96,689 × 96,689
  4. Step 4: Simplify right side
    83,513x = 9,348,762,721
  5. Step 5: Solve for x
    x = 9,348,762,721/83,513
  6. Step 6: Final answer
    x = 111,943.80

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Why These Related Problems?

These problems maintain the same ratio (1.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.