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Finding the Third Proportional to 102,651 and 164,517

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Solution

The third proportional to 102,651 and 164,517 is: 263,668.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    102,651 : 164,517 = 164,517 : x
  2. Step 2: Convert to fraction form
    102,651/164,517 = 164,517/x
  3. Step 3: Cross multiply
    102,651x = 164,517 × 164,517
  4. Step 4: Simplify right side
    102,651x = 27,065,843,289
  5. Step 5: Solve for x
    x = 27,065,843,289/102,651
  6. Step 6: Final answer
    x = 263,668.58

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.