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Finding the Third Proportional to 6,502.78 and 7,824.09

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Solution

The third proportional to 6,502.78 and 7,824.09 is: 9,413.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,502.78 : 7,824.09 = 7,824.09 : x
  2. Step 2: Convert to fraction form
    6,502.78/7,824.09 = 7,824.09/x
  3. Step 3: Cross multiply
    6,502.78x = 7,824.09 × 7,824.09
  4. Step 4: Simplify right side
    6,502.78x = 61,216,443.01
  5. Step 5: Solve for x
    x = 61,216,443.01/6,502.78
  6. Step 6: Final answer
    x = 9,413.89

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Why These Related Problems?

These problems maintain the same ratio (1.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.