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Finding the Third Proportional to 8,649 and 9,537

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Solution

The third proportional to 8,649 and 9,537 is: 10,516.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,649 : 9,537 = 9,537 : x
  2. Step 2: Convert to fraction form
    8,649/9,537 = 9,537/x
  3. Step 3: Cross multiply
    8,649x = 9,537 × 9,537
  4. Step 4: Simplify right side
    8,649x = 90,954,369
  5. Step 5: Solve for x
    x = 90,954,369/8,649
  6. Step 6: Final answer
    x = 10,516.17

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.