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Finding the Third Proportional to 106,566 and 177,591

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Solution

The third proportional to 106,566 and 177,591 is: 295,953.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,566 : 177,591 = 177,591 : x
  2. Step 2: Convert to fraction form
    106,566/177,591 = 177,591/x
  3. Step 3: Cross multiply
    106,566x = 177,591 × 177,591
  4. Step 4: Simplify right side
    106,566x = 31,538,563,281
  5. Step 5: Solve for x
    x = 31,538,563,281/106,566
  6. Step 6: Final answer
    x = 295,953.34

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Why These Related Problems?

These problems maintain the same ratio (1.67) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.