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Finding the Third Proportional to 6,509 and 15,746

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Solution

The third proportional to 6,509 and 15,746 is: 38,091.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,509 : 15,746 = 15,746 : x
  2. Step 2: Convert to fraction form
    6,509/15,746 = 15,746/x
  3. Step 3: Cross multiply
    6,509x = 15,746 × 15,746
  4. Step 4: Simplify right side
    6,509x = 247,936,516
  5. Step 5: Solve for x
    x = 247,936,516/6,509
  6. Step 6: Final answer
    x = 38,091.34

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Why These Related Problems?

These problems maintain the same ratio (2.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.