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Finding the Third Proportional to 51,734 and 82,658

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Solution

The third proportional to 51,734 and 82,658 is: 132,066.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,734 : 82,658 = 82,658 : x
  2. Step 2: Convert to fraction form
    51,734/82,658 = 82,658/x
  3. Step 3: Cross multiply
    51,734x = 82,658 × 82,658
  4. Step 4: Simplify right side
    51,734x = 6,832,344,964
  5. Step 5: Solve for x
    x = 6,832,344,964/51,734
  6. Step 6: Final answer
    x = 132,066.82

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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.