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Finding the Third Proportional to 4,160 and 8,509

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Solution

The third proportional to 4,160 and 8,509 is: 17,404.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,160 : 8,509 = 8,509 : x
  2. Step 2: Convert to fraction form
    4,160/8,509 = 8,509/x
  3. Step 3: Cross multiply
    4,160x = 8,509 × 8,509
  4. Step 4: Simplify right side
    4,160x = 72,403,081
  5. Step 5: Solve for x
    x = 72,403,081/4,160
  6. Step 6: Final answer
    x = 17,404.59

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Why These Related Problems?

These problems maintain the same ratio (2.05) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.