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Finding the Third Proportional to 83,788 and 117,206

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Solution

The third proportional to 83,788 and 117,206 is: 163,952.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,788 : 117,206 = 117,206 : x
  2. Step 2: Convert to fraction form
    83,788/117,206 = 117,206/x
  3. Step 3: Cross multiply
    83,788x = 117,206 × 117,206
  4. Step 4: Simplify right side
    83,788x = 13,737,246,436
  5. Step 5: Solve for x
    x = 13,737,246,436/83,788
  6. Step 6: Final answer
    x = 163,952.43

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.