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Finding the Third Proportional to 9,677 and 19,764

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Solution

The third proportional to 9,677 and 19,764 is: 40,365.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,677 : 19,764 = 19,764 : x
  2. Step 2: Convert to fraction form
    9,677/19,764 = 19,764/x
  3. Step 3: Cross multiply
    9,677x = 19,764 × 19,764
  4. Step 4: Simplify right side
    9,677x = 390,615,696
  5. Step 5: Solve for x
    x = 390,615,696/9,677
  6. Step 6: Final answer
    x = 40,365.37

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Why These Related Problems?

These problems maintain the same ratio (2.04) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.