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Finding the Third Proportional to 8,500 and 9,736

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Solution

The third proportional to 8,500 and 9,736 is: 11,151.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,500 : 9,736 = 9,736 : x
  2. Step 2: Convert to fraction form
    8,500/9,736 = 9,736/x
  3. Step 3: Cross multiply
    8,500x = 9,736 × 9,736
  4. Step 4: Simplify right side
    8,500x = 94,789,696
  5. Step 5: Solve for x
    x = 94,789,696/8,500
  6. Step 6: Final answer
    x = 11,151.73

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.