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Finding the Third Proportional to 51,774 and 77,581

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Solution

The third proportional to 51,774 and 77,581 is: 116,251.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,774 : 77,581 = 77,581 : x
  2. Step 2: Convert to fraction form
    51,774/77,581 = 77,581/x
  3. Step 3: Cross multiply
    51,774x = 77,581 × 77,581
  4. Step 4: Simplify right side
    51,774x = 6,018,811,561
  5. Step 5: Solve for x
    x = 6,018,811,561/51,774
  6. Step 6: Final answer
    x = 116,251.62

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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.