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Finding the Third Proportional to 6,530 and 9,825

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Solution

The third proportional to 6,530 and 9,825 is: 14,782.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,530 : 9,825 = 9,825 : x
  2. Step 2: Convert to fraction form
    6,530/9,825 = 9,825/x
  3. Step 3: Cross multiply
    6,530x = 9,825 × 9,825
  4. Step 4: Simplify right side
    6,530x = 96,530,625
  5. Step 5: Solve for x
    x = 96,530,625/6,530
  6. Step 6: Final answer
    x = 14,782.64

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.