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Finding the Third Proportional to 83,657 and 180,346

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Solution

The third proportional to 83,657 and 180,346 is: 388,786.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,657 : 180,346 = 180,346 : x
  2. Step 2: Convert to fraction form
    83,657/180,346 = 180,346/x
  3. Step 3: Cross multiply
    83,657x = 180,346 × 180,346
  4. Step 4: Simplify right side
    83,657x = 32,524,679,716
  5. Step 5: Solve for x
    x = 32,524,679,716/83,657
  6. Step 6: Final answer
    x = 388,786.11

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.