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Finding the Third Proportional to 7,684 and 8,420

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Solution

The third proportional to 7,684 and 8,420 is: 9,226.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,684 : 8,420 = 8,420 : x
  2. Step 2: Convert to fraction form
    7,684/8,420 = 8,420/x
  3. Step 3: Cross multiply
    7,684x = 8,420 × 8,420
  4. Step 4: Simplify right side
    7,684x = 70,896,400
  5. Step 5: Solve for x
    x = 70,896,400/7,684
  6. Step 6: Final answer
    x = 9,226.50

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.