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Finding the Third Proportional to 6,614 and 9,506

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Solution

The third proportional to 6,614 and 9,506 is: 13,662.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,614 : 9,506 = 9,506 : x
  2. Step 2: Convert to fraction form
    6,614/9,506 = 9,506/x
  3. Step 3: Cross multiply
    6,614x = 9,506 × 9,506
  4. Step 4: Simplify right side
    6,614x = 90,364,036
  5. Step 5: Solve for x
    x = 90,364,036/6,614
  6. Step 6: Final answer
    x = 13,662.54

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Why These Related Problems?

These problems maintain the same ratio (1.44) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.