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Finding the Third Proportional to 38,506 and 82,742

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Solution

The third proportional to 38,506 and 82,742 is: 177,796.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    38,506 : 82,742 = 82,742 : x
  2. Step 2: Convert to fraction form
    38,506/82,742 = 82,742/x
  3. Step 3: Cross multiply
    38,506x = 82,742 × 82,742
  4. Step 4: Simplify right side
    38,506x = 6,846,238,564
  5. Step 5: Solve for x
    x = 6,846,238,564/38,506
  6. Step 6: Final answer
    x = 177,796.67

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.