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Finding the Third Proportional to 83 and 109

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Solution

The third proportional to 83 and 109 is: 143.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    83 : 109 = 109 : x
  2. Step 2: Convert to fraction form
    83/109 = 109/x
  3. Step 3: Cross multiply
    83x = 109 × 109
  4. Step 4: Simplify right side
    83x = 11,881
  5. Step 5: Solve for x
    x = 11,881/83
  6. Step 6: Final answer
    x = 143.14

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Why These Related Problems?

These problems maintain the same ratio (1.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.