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Finding the Third Proportional to 4,977 and 6,561

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Solution

The third proportional to 4,977 and 6,561 is: 8,649.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,977 : 6,561 = 6,561 : x
  2. Step 2: Convert to fraction form
    4,977/6,561 = 6,561/x
  3. Step 3: Cross multiply
    4,977x = 6,561 × 6,561
  4. Step 4: Simplify right side
    4,977x = 43,046,721
  5. Step 5: Solve for x
    x = 43,046,721/4,977
  6. Step 6: Final answer
    x = 8,649.13

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Why These Related Problems?

These problems maintain the same ratio (1.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.