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Finding the Third Proportional to 51,006 and 76,509

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Solution

The third proportional to 51,006 and 76,509 is: 114,763.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,006 : 76,509 = 76,509 : x
  2. Step 2: Convert to fraction form
    51,006/76,509 = 76,509/x
  3. Step 3: Cross multiply
    51,006x = 76,509 × 76,509
  4. Step 4: Simplify right side
    51,006x = 5,853,627,081
  5. Step 5: Solve for x
    x = 5,853,627,081/51,006
  6. Step 6: Final answer
    x = 114,763.50

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.