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Finding the Third Proportional to 71,776 and 102,742

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Solution

The third proportional to 71,776 and 102,742 is: 147,067.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    71,776 : 102,742 = 102,742 : x
  2. Step 2: Convert to fraction form
    71,776/102,742 = 102,742/x
  3. Step 3: Cross multiply
    71,776x = 102,742 × 102,742
  4. Step 4: Simplify right side
    71,776x = 10,555,918,564
  5. Step 5: Solve for x
    x = 10,555,918,564/71,776
  6. Step 6: Final answer
    x = 147,067.52

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.