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Finding the Third Proportional to 7,781 and 11,677

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Solution

The third proportional to 7,781 and 11,677 is: 17,523.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,781 : 11,677 = 11,677 : x
  2. Step 2: Convert to fraction form
    7,781/11,677 = 11,677/x
  3. Step 3: Cross multiply
    7,781x = 11,677 × 11,677
  4. Step 4: Simplify right side
    7,781x = 136,352,329
  5. Step 5: Solve for x
    x = 136,352,329/7,781
  6. Step 6: Final answer
    x = 17,523.75

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.