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Finding the Third Proportional to 8,424 and 9,864

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Solution

The third proportional to 8,424 and 9,864 is: 11,550.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,424 : 9,864 = 9,864 : x
  2. Step 2: Convert to fraction form
    8,424/9,864 = 9,864/x
  3. Step 3: Cross multiply
    8,424x = 9,864 × 9,864
  4. Step 4: Simplify right side
    8,424x = 97,298,496
  5. Step 5: Solve for x
    x = 97,298,496/8,424
  6. Step 6: Final answer
    x = 11,550.15

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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.