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Finding the Third Proportional to 6,505 and 14,306

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Solution

The third proportional to 6,505 and 14,306 is: 31,462.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,505 : 14,306 = 14,306 : x
  2. Step 2: Convert to fraction form
    6,505/14,306 = 14,306/x
  3. Step 3: Cross multiply
    6,505x = 14,306 × 14,306
  4. Step 4: Simplify right side
    6,505x = 204,661,636
  5. Step 5: Solve for x
    x = 204,661,636/6,505
  6. Step 6: Final answer
    x = 31,462.20

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.