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Finding the Third Proportional to 6,540 and 13,524

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Solution

The third proportional to 6,540 and 13,524 is: 27,966.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,540 : 13,524 = 13,524 : x
  2. Step 2: Convert to fraction form
    6,540/13,524 = 13,524/x
  3. Step 3: Cross multiply
    6,540x = 13,524 × 13,524
  4. Step 4: Simplify right side
    6,540x = 182,898,576
  5. Step 5: Solve for x
    x = 182,898,576/6,540
  6. Step 6: Final answer
    x = 27,966.14

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Why These Related Problems?

These problems maintain the same ratio (2.07) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.