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Finding the Third Proportional to 6,501 and 14,097

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Solution

The third proportional to 6,501 and 14,097 is: 30,568.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,501 : 14,097 = 14,097 : x
  2. Step 2: Convert to fraction form
    6,501/14,097 = 14,097/x
  3. Step 3: Cross multiply
    6,501x = 14,097 × 14,097
  4. Step 4: Simplify right side
    6,501x = 198,725,409
  5. Step 5: Solve for x
    x = 198,725,409/6,501
  6. Step 6: Final answer
    x = 30,568.44

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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.