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Finding the Third Proportional to 7,724 and 8,696

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Solution

The third proportional to 7,724 and 8,696 is: 9,790.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,724 : 8,696 = 8,696 : x
  2. Step 2: Convert to fraction form
    7,724/8,696 = 8,696/x
  3. Step 3: Cross multiply
    7,724x = 8,696 × 8,696
  4. Step 4: Simplify right side
    7,724x = 75,620,416
  5. Step 5: Solve for x
    x = 75,620,416/7,724
  6. Step 6: Final answer
    x = 9,790.32

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Why These Related Problems?

These problems maintain the same ratio (1.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.