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Finding the Third Proportional to 42,102 and 97,461

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Solution

The third proportional to 42,102 and 97,461 is: 225,610.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    42,102 : 97,461 = 97,461 : x
  2. Step 2: Convert to fraction form
    42,102/97,461 = 97,461/x
  3. Step 3: Cross multiply
    42,102x = 97,461 × 97,461
  4. Step 4: Simplify right side
    42,102x = 9,498,646,521
  5. Step 5: Solve for x
    x = 9,498,646,521/42,102
  6. Step 6: Final answer
    x = 225,610.34

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Why These Related Problems?

These problems maintain the same ratio (2.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.