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Finding the Third Proportional to 75,684 and 164,468

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Solution

The third proportional to 75,684 and 164,468 is: 357,403.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    75,684 : 164,468 = 164,468 : x
  2. Step 2: Convert to fraction form
    75,684/164,468 = 164,468/x
  3. Step 3: Cross multiply
    75,684x = 164,468 × 164,468
  4. Step 4: Simplify right side
    75,684x = 27,049,723,024
  5. Step 5: Solve for x
    x = 27,049,723,024/75,684
  6. Step 6: Final answer
    x = 357,403.45

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.