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Finding the Third Proportional to 51,357 and 76,830

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Solution

The third proportional to 51,357 and 76,830 is: 114,937.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,357 : 76,830 = 76,830 : x
  2. Step 2: Convert to fraction form
    51,357/76,830 = 76,830/x
  3. Step 3: Cross multiply
    51,357x = 76,830 × 76,830
  4. Step 4: Simplify right side
    51,357x = 5,902,848,900
  5. Step 5: Solve for x
    x = 5,902,848,900/51,357
  6. Step 6: Final answer
    x = 114,937.57

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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.