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Finding the Third Proportional to 6,580 and 10,214

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Solution

The third proportional to 6,580 and 10,214 is: 15,854.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,580 : 10,214 = 10,214 : x
  2. Step 2: Convert to fraction form
    6,580/10,214 = 10,214/x
  3. Step 3: Cross multiply
    6,580x = 10,214 × 10,214
  4. Step 4: Simplify right side
    6,580x = 104,325,796
  5. Step 5: Solve for x
    x = 104,325,796/6,580
  6. Step 6: Final answer
    x = 15,854.98

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.