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Finding the Third Proportional to 6,586 and 14,324

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Solution

The third proportional to 6,586 and 14,324 is: 31,153.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,586 : 14,324 = 14,324 : x
  2. Step 2: Convert to fraction form
    6,586/14,324 = 14,324/x
  3. Step 3: Cross multiply
    6,586x = 14,324 × 14,324
  4. Step 4: Simplify right side
    6,586x = 205,176,976
  5. Step 5: Solve for x
    x = 205,176,976/6,586
  6. Step 6: Final answer
    x = 31,153.50

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.