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Finding the Third Proportional to 7,720 and 8,456

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Solution

The third proportional to 7,720 and 8,456 is: 9,262.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,720 : 8,456 = 8,456 : x
  2. Step 2: Convert to fraction form
    7,720/8,456 = 8,456/x
  3. Step 3: Cross multiply
    7,720x = 8,456 × 8,456
  4. Step 4: Simplify right side
    7,720x = 71,503,936
  5. Step 5: Solve for x
    x = 71,503,936/7,720
  6. Step 6: Final answer
    x = 9,262.17

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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.