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Finding the Third Proportional to 6,500 and 9,814

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Solution

The third proportional to 6,500 and 9,814 is: 14,817.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,500 : 9,814 = 9,814 : x
  2. Step 2: Convert to fraction form
    6,500/9,814 = 9,814/x
  3. Step 3: Cross multiply
    6,500x = 9,814 × 9,814
  4. Step 4: Simplify right side
    6,500x = 96,314,596
  5. Step 5: Solve for x
    x = 96,314,596/6,500
  6. Step 6: Final answer
    x = 14,817.63

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.