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Finding the Third Proportional to 51,678 and 77,517

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Solution

The third proportional to 51,678 and 77,517 is: 116,275.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,678 : 77,517 = 77,517 : x
  2. Step 2: Convert to fraction form
    51,678/77,517 = 77,517/x
  3. Step 3: Cross multiply
    51,678x = 77,517 × 77,517
  4. Step 4: Simplify right side
    51,678x = 6,008,885,289
  5. Step 5: Solve for x
    x = 6,008,885,289/51,678
  6. Step 6: Final answer
    x = 116,275.50

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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.