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Finding the Third Proportional to 5,969 and 13,777

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Solution

The third proportional to 5,969 and 13,777 is: 31,798.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,969 : 13,777 = 13,777 : x
  2. Step 2: Convert to fraction form
    5,969/13,777 = 13,777/x
  3. Step 3: Cross multiply
    5,969x = 13,777 × 13,777
  4. Step 4: Simplify right side
    5,969x = 189,805,729
  5. Step 5: Solve for x
    x = 189,805,729/5,969
  6. Step 6: Final answer
    x = 31,798.58

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Why These Related Problems?

These problems maintain the same ratio (2.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.