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Finding the Third Proportional to 2,561 and 4,077

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Solution

The third proportional to 2,561 and 4,077 is: 6,490.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,561 : 4,077 = 4,077 : x
  2. Step 2: Convert to fraction form
    2,561/4,077 = 4,077/x
  3. Step 3: Cross multiply
    2,561x = 4,077 × 4,077
  4. Step 4: Simplify right side
    2,561x = 16,621,929
  5. Step 5: Solve for x
    x = 16,621,929/2,561
  6. Step 6: Final answer
    x = 6,490.41

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.