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Finding the Third Proportional to 53,097 and 82,431

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Solution

The third proportional to 53,097 and 82,431 is: 127,970.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    53,097 : 82,431 = 82,431 : x
  2. Step 2: Convert to fraction form
    53,097/82,431 = 82,431/x
  3. Step 3: Cross multiply
    53,097x = 82,431 × 82,431
  4. Step 4: Simplify right side
    53,097x = 6,794,869,761
  5. Step 5: Solve for x
    x = 6,794,869,761/53,097
  6. Step 6: Final answer
    x = 127,970.88

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.