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Finding the Third Proportional to 6,864 and 7,824

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Solution

The third proportional to 6,864 and 7,824 is: 8,918.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,864 : 7,824 = 7,824 : x
  2. Step 2: Convert to fraction form
    6,864/7,824 = 7,824/x
  3. Step 3: Cross multiply
    6,864x = 7,824 × 7,824
  4. Step 4: Simplify right side
    6,864x = 61,214,976
  5. Step 5: Solve for x
    x = 61,214,976/6,864
  6. Step 6: Final answer
    x = 8,918.27

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.