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Finding the Third Proportional to 42,096 and 97,464

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Solution

The third proportional to 42,096 and 97,464 is: 225,656.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    42,096 : 97,464 = 97,464 : x
  2. Step 2: Convert to fraction form
    42,096/97,464 = 97,464/x
  3. Step 3: Cross multiply
    42,096x = 97,464 × 97,464
  4. Step 4: Simplify right side
    42,096x = 9,499,231,296
  5. Step 5: Solve for x
    x = 9,499,231,296/42,096
  6. Step 6: Final answer
    x = 225,656.39

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.