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Finding the Third Proportional to 83,284 and 133,206

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Solution

The third proportional to 83,284 and 133,206 is: 213,052.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,284 : 133,206 = 133,206 : x
  2. Step 2: Convert to fraction form
    83,284/133,206 = 133,206/x
  3. Step 3: Cross multiply
    83,284x = 133,206 × 133,206
  4. Step 4: Simplify right side
    83,284x = 17,743,838,436
  5. Step 5: Solve for x
    x = 17,743,838,436/83,284
  6. Step 6: Final answer
    x = 213,052.19

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.