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Finding the Third Proportional to 51,730 and 82,651

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Solution

The third proportional to 51,730 and 82,651 is: 132,054.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,730 : 82,651 = 82,651 : x
  2. Step 2: Convert to fraction form
    51,730/82,651 = 82,651/x
  3. Step 3: Cross multiply
    51,730x = 82,651 × 82,651
  4. Step 4: Simplify right side
    51,730x = 6,831,187,801
  5. Step 5: Solve for x
    x = 6,831,187,801/51,730
  6. Step 6: Final answer
    x = 132,054.66

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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.