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Finding the Third Proportional to 51,786 and 75,977

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Solution

The third proportional to 51,786 and 75,977 is: 111,468.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,786 : 75,977 = 75,977 : x
  2. Step 2: Convert to fraction form
    51,786/75,977 = 75,977/x
  3. Step 3: Cross multiply
    51,786x = 75,977 × 75,977
  4. Step 4: Simplify right side
    51,786x = 5,772,504,529
  5. Step 5: Solve for x
    x = 5,772,504,529/51,786
  6. Step 6: Final answer
    x = 111,468.44

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.