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Finding the Third Proportional to 120,972 and 257,496

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Solution

The third proportional to 120,972 and 257,496 is: 548,095.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    120,972 : 257,496 = 257,496 : x
  2. Step 2: Convert to fraction form
    120,972/257,496 = 257,496/x
  3. Step 3: Cross multiply
    120,972x = 257,496 × 257,496
  4. Step 4: Simplify right side
    120,972x = 66,304,190,016
  5. Step 5: Solve for x
    x = 66,304,190,016/120,972
  6. Step 6: Final answer
    x = 548,095.34

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.