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Finding the Third Proportional to 8,300 and 9,677

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Solution

The third proportional to 8,300 and 9,677 is: 11,282.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,300 : 9,677 = 9,677 : x
  2. Step 2: Convert to fraction form
    8,300/9,677 = 9,677/x
  3. Step 3: Cross multiply
    8,300x = 9,677 × 9,677
  4. Step 4: Simplify right side
    8,300x = 93,644,329
  5. Step 5: Solve for x
    x = 93,644,329/8,300
  6. Step 6: Final answer
    x = 11,282.45

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Why These Related Problems?

These problems maintain the same ratio (1.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.