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Finding the Third Proportional to 6,403 and 13,777

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Solution

The third proportional to 6,403 and 13,777 is: 29,643.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,403 : 13,777 = 13,777 : x
  2. Step 2: Convert to fraction form
    6,403/13,777 = 13,777/x
  3. Step 3: Cross multiply
    6,403x = 13,777 × 13,777
  4. Step 4: Simplify right side
    6,403x = 189,805,729
  5. Step 5: Solve for x
    x = 189,805,729/6,403
  6. Step 6: Final answer
    x = 29,643.25

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.