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Finding the Third Proportional to 7,734 and 16,561

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Solution

The third proportional to 7,734 and 16,561 is: 35,462.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,734 : 16,561 = 16,561 : x
  2. Step 2: Convert to fraction form
    7,734/16,561 = 16,561/x
  3. Step 3: Cross multiply
    7,734x = 16,561 × 16,561
  4. Step 4: Simplify right side
    7,734x = 274,266,721
  5. Step 5: Solve for x
    x = 274,266,721/7,734
  6. Step 6: Final answer
    x = 35,462.47

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.