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Finding the Third Proportional to 6,509 and 13,880

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Solution

The third proportional to 6,509 and 13,880 is: 29,598.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,509 : 13,880 = 13,880 : x
  2. Step 2: Convert to fraction form
    6,509/13,880 = 13,880/x
  3. Step 3: Cross multiply
    6,509x = 13,880 × 13,880
  4. Step 4: Simplify right side
    6,509x = 192,654,400
  5. Step 5: Solve for x
    x = 192,654,400/6,509
  6. Step 6: Final answer
    x = 29,598.16

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.