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Finding the Third Proportional to 3,234 and 8,409

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Solution

The third proportional to 3,234 and 8,409 is: 21,864.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,234 : 8,409 = 8,409 : x
  2. Step 2: Convert to fraction form
    3,234/8,409 = 8,409/x
  3. Step 3: Cross multiply
    3,234x = 8,409 × 8,409
  4. Step 4: Simplify right side
    3,234x = 70,711,281
  5. Step 5: Solve for x
    x = 70,711,281/3,234
  6. Step 6: Final answer
    x = 21,864.96

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Why These Related Problems?

These problems maintain the same ratio (2.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.