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Finding the Third Proportional to 51,828 and 82,509

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Solution

The third proportional to 51,828 and 82,509 is: 131,352.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,828 : 82,509 = 82,509 : x
  2. Step 2: Convert to fraction form
    51,828/82,509 = 82,509/x
  3. Step 3: Cross multiply
    51,828x = 82,509 × 82,509
  4. Step 4: Simplify right side
    51,828x = 6,807,735,081
  5. Step 5: Solve for x
    x = 6,807,735,081/51,828
  6. Step 6: Final answer
    x = 131,352.46

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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.