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Finding the Third Proportional to 6,214 and 9,201

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Solution

The third proportional to 6,214 and 9,201 is: 13,623.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,214 : 9,201 = 9,201 : x
  2. Step 2: Convert to fraction form
    6,214/9,201 = 9,201/x
  3. Step 3: Cross multiply
    6,214x = 9,201 × 9,201
  4. Step 4: Simplify right side
    6,214x = 84,658,401
  5. Step 5: Solve for x
    x = 84,658,401/6,214
  6. Step 6: Final answer
    x = 13,623.82

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Why These Related Problems?

These problems maintain the same ratio (1.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.