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Finding the Third Proportional to 97,096 and 208,412

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Solution

The third proportional to 97,096 and 208,412 is: 447,346.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,096 : 208,412 = 208,412 : x
  2. Step 2: Convert to fraction form
    97,096/208,412 = 208,412/x
  3. Step 3: Cross multiply
    97,096x = 208,412 × 208,412
  4. Step 4: Simplify right side
    97,096x = 43,435,561,744
  5. Step 5: Solve for x
    x = 43,435,561,744/97,096
  6. Step 6: Final answer
    x = 447,346.56

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.