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Finding the Third Proportional to 106,314 and 164,511

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Solution

The third proportional to 106,314 and 164,511 is: 254,565.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,314 : 164,511 = 164,511 : x
  2. Step 2: Convert to fraction form
    106,314/164,511 = 164,511/x
  3. Step 3: Cross multiply
    106,314x = 164,511 × 164,511
  4. Step 4: Simplify right side
    106,314x = 27,063,869,121
  5. Step 5: Solve for x
    x = 27,063,869,121/106,314
  6. Step 6: Final answer
    x = 254,565.43

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.