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Finding the Third Proportional to 83,224 and 135,209

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Solution

The third proportional to 83,224 and 135,209 is: 219,665.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,224 : 135,209 = 135,209 : x
  2. Step 2: Convert to fraction form
    83,224/135,209 = 135,209/x
  3. Step 3: Cross multiply
    83,224x = 135,209 × 135,209
  4. Step 4: Simplify right side
    83,224x = 18,281,473,681
  5. Step 5: Solve for x
    x = 18,281,473,681/83,224
  6. Step 6: Final answer
    x = 219,665.89

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Why These Related Problems?

These problems maintain the same ratio (1.62) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.