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Finding the Third Proportional to 6,864 and 7,416

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Solution

The third proportional to 6,864 and 7,416 is: 8,012.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,864 : 7,416 = 7,416 : x
  2. Step 2: Convert to fraction form
    6,864/7,416 = 7,416/x
  3. Step 3: Cross multiply
    6,864x = 7,416 × 7,416
  4. Step 4: Simplify right side
    6,864x = 54,997,056
  5. Step 5: Solve for x
    x = 54,997,056/6,864
  6. Step 6: Final answer
    x = 8,012.39

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.