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Finding the Third Proportional to 49,434 and 102,964

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Solution

The third proportional to 49,434 and 102,964 is: 214,459.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    49,434 : 102,964 = 102,964 : x
  2. Step 2: Convert to fraction form
    49,434/102,964 = 102,964/x
  3. Step 3: Cross multiply
    49,434x = 102,964 × 102,964
  4. Step 4: Simplify right side
    49,434x = 10,601,585,296
  5. Step 5: Solve for x
    x = 10,601,585,296/49,434
  6. Step 6: Final answer
    x = 214,459.39

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.