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Finding the Third Proportional to 38,214 and 83,809

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Solution

The third proportional to 38,214 and 83,809 is: 183,805.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    38,214 : 83,809 = 83,809 : x
  2. Step 2: Convert to fraction form
    38,214/83,809 = 83,809/x
  3. Step 3: Cross multiply
    38,214x = 83,809 × 83,809
  4. Step 4: Simplify right side
    38,214x = 7,023,948,481
  5. Step 5: Solve for x
    x = 7,023,948,481/38,214
  6. Step 6: Final answer
    x = 183,805.63

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.