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Finding the Third Proportional to 51,706 and 82,007

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Solution

The third proportional to 51,706 and 82,007 is: 130,065.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,706 : 82,007 = 82,007 : x
  2. Step 2: Convert to fraction form
    51,706/82,007 = 82,007/x
  3. Step 3: Cross multiply
    51,706x = 82,007 × 82,007
  4. Step 4: Simplify right side
    51,706x = 6,725,148,049
  5. Step 5: Solve for x
    x = 6,725,148,049/51,706
  6. Step 6: Final answer
    x = 130,065.14

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.