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Finding the Third Proportional to 6,500 and 9,714

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Solution

The third proportional to 6,500 and 9,714 is: 14,517.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,500 : 9,714 = 9,714 : x
  2. Step 2: Convert to fraction form
    6,500/9,714 = 9,714/x
  3. Step 3: Cross multiply
    6,500x = 9,714 × 9,714
  4. Step 4: Simplify right side
    6,500x = 94,361,796
  5. Step 5: Solve for x
    x = 94,361,796/6,500
  6. Step 6: Final answer
    x = 14,517.20

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.